how to find the square root of a fraction
Square Root
The foursquare root of a number is the inverse operation of squaring a number. The foursquare of a number is the value that is obtained when we multiply the number past itself, while the square root of a number is the factor of a number which when multiplied by itself gives the original number. If 'a' is the square root of 'b', it means that a × a = b. The square of any number is ever a positive number, so every number has 2 foursquare roots, one of a positive value, and one of a negative value. For example, both 2 and -2 are square roots of 4. However, in well-nigh places, merely the positive value is written as the square root of a number.
| 1. | What is Square Root? |
| two. | How to discover Square Root? |
| 3. | Foursquare Root Table |
| iv. | Foursquare Root Formula |
| 5. | How to Simplify Square Root? |
| 6. | Square Root of a Negative Number |
| seven. | Square of a Number |
| 8. | How to Find Square of a Number? |
| ix. | FAQs on Square Root |
What is Square Root?
The square root of a number is that factor of a number which when multiplied past itself gives the original number. Squares and square roots are special exponents. Consider the number nine. When iii is multiplied by itself, information technology gives 9 every bit the product. This can be written as 3 × 3 or three2. Here, the exponent is ii, and nosotros phone call information technology a square. Now when the exponent is 1/2, it refers to the foursquare root of the number. For example √(northward × n) = √ntwo = north, where north is a positive integer.
Square Root Definition
The square root of a number is the value of power one/2 of that number. In other words, information technology is the number that nosotros multiply by itself to get the original number. It is represented using the symbol '√ '. The square root symbol is called the radical, whereas the number under the foursquare root symbol is called the radicand that is used to stand for the foursquare root of any natural number.
How to Find Square Root?
It is very easy to observe the square root of a number that is a perfect square. Perfect squares are those positive numbers that can be expressed as the product of a number by itself. in other words, perfect squares are numbers which are expressed equally the value of power two of whatever integer. We tin can use four methods to find the square root of numbers and those methods are as follows:
- Repeated Subtraction Method of Foursquare Root
- Foursquare Root past Prime Factorization Method
- Square Root by Estimation Method
- Square Root by Long Division Method
Information technology should be noted that the start iii methods tin can be conveniently used for perfect squares, while the fourth method, i.e., the long partition method can be used for whatever number whether information technology is a perfect foursquare or not.
Repeated Subtraction Method of Square Root
This is a very uncomplicated method. We decrease the sequent odd numbers from the number for which we are finding the square root, till we reach 0. The number of times nosotros subtract is the foursquare root of the given number. This method works just for perfect foursquare numbers. Let us find the square root of sixteen using this method.
- 16 - 1 = 15
- 15 - 3 =12
- 12 - five = vii
- 7- 7 = 0
You can observe that we have subtracted 4 times. Thus,√16 = 4
Square Root by Prime Factorization Method
Prime factorization of whatsoever number means to represent that number as a product of prime numbers. To observe the square root of a given number through the prime factorization method, nosotros follow the steps given below:
- Step i: Divide the given number into its prime factors.
- Step 2: Class pairs of similar factors such that both factors in each pair are equal.
- Step 3: Take i factor from the pair.
- Footstep iv: Observe the product of the factors obtained by taking ane gene from each pair.
- Footstep 5: That product is the square root of the given number.
Let united states of america find the square root of 144 by this method.
This method works when the given number is a perfect square number.
Foursquare Root by Estimation Method
Estimation and approximation refer to a reasonable guess of the bodily value to make calculations easier and more realistic. This method helps in estimating and approximating the square root of a given number. Permit us use this method to detect √15. Find the nearest perfect square numbers to fifteen. ix and sixteen are the perfect square numbers nearest to 15. Nosotros know that √sixteen = 4 and √9 = three. This implies that √xv lies between three and 4. At present, nosotros need to come across if √15 is closer to three or 4. Let united states consider 3.v and 4. Since 3.52 = 12.25 and 42= xvi. Thus, √fifteen lies between 3.5 and 4 and is closer to 4.
Permit us find the squares of iii.8 and iii.9. Since 3.8ii = 14.44 and 3.ix2 = 15.21. This implies that √15 lies between 3.8 and iii.9. We can echo the process and check between iii.85 and 3.9. We can observe that √15 = 3.872.
This is a very long process and time-consuming.
Square Root by Long Division Method
Long Division is a method for dividing large numbers into steps or parts, breaking the partitioning problem into a sequence of easier steps. We tin can find the verbal square root of whatever given number using this method. Let us understand the process of finding foursquare root by the long division method with an instance. Let us find the square root of 180.
- Step one: Place a bar over every pair of digits of the number starting from the units' place (correct-most side). We will have two pairs, i.due east., 1 and 80
- Step ii: We divide the left-most number past the largest number whose square is less than or equal to the number in the left-nigh pair.
Pace 3: Bring downwards the number under the next bar to the right of the residue. Add the terminal digit of the caliber to the divisor. To the right of the obtained sum, notice a suitable number which, together with the result of the sum, forms a new divisor for the new dividend that is carried down.
Step 4: The new number in the quotient volition take the same number as selected in the divisor. The condition is the same — as being either less than or equal to the dividend.
Step v: Now, nosotros will proceed this process further using a decimal point and adding zeros in pairs to the residual.
Pace half-dozen: The quotient thus obtained will be the foursquare root of the number.
Foursquare Root Table
The square root table consists of numbers and their square roots. It is useful to find the squares of numbers as well. Here is the list of square roots of perfect square numbers and some non-perfect foursquare numbers from 1 to ten.
| Number | Square Root |
|---|---|
| 1 | 1 |
| 2 | 1.414 |
| 3 | one.732 |
| 4 | 2 |
| 5 | two.236 |
| six | 2.449 |
| 7 | 2.646 |
| viii | 2.828 |
| 9 | 3 |
| ten | three.162 |
The square roots of numbers that are non perfect squares are part of irrational numbers.
Square Root Formula
The foursquare root of a number has the exponent of one/2. The square root formula is used to find the foursquare root of a number. We know the exponent formula: \(\sqrt[\text{north}]{x}\) = x1/n. When n= 2, we call it square root. We can employ any of the in a higher place methods for finding the square root, such every bit prime number factorization, long division, and so on. 91/2 = √ix = √(three×iii) = three. So, the formula for writing the square root of a number is √x= xone/2.
How to Simplify Square Root?
To simplify a square root, nosotros need to detect the prime factorization of the given number. If a cistron cannot be grouped, retain them nether the foursquare root symbol. The rule of simplifying square root is √xy = √(x × y), where, x and y are positive integers. For example: √12 = \(\sqrt{2 \times 2\times3}\) = 2√3
For fractions, there is too a like dominion: √x/√y = √(x/y). For example: √50/√10 = √(50/x)= √5
Square Root of a Negative Number
The square root of a negative number cannot be a real number, since a foursquare is either a positive number or zero. Merely complex numbers accept the solutions to the square root of a negative number. The principal square root of -x is: √(-x)= i√x. Here, i is the square root of -ane.
For case: Take a perfect square number similar 16. Now, let'south see the square root of -16. There is no real square root of -sixteen. √(-16)= √16 × √(-ane) = 4i (every bit, √(-1)= i), where 'i' is represented equally the square root of -1. So, 4i is a foursquare root of -sixteen.
Foursquare of a Number
Any number raised to exponent two (ytwo) is called the square of the base. So, 52 or 25 is referred to as the square of 5, while 82 or 64 is referred to as the square of 8. We can easily find the square of a number by multiplying the number two times. For case, 52 = 5 × 5 = 25, and 82 = 8 × eight = 64. When we find the square of a whole number, the resultant number is a perfect square. Some of the perfect squares we have are 4, 9, 16, 25, 36, 49, 64, and then on. The square of a number is always a positive number.
How to Find the Square of a Number?
The square of a number can be constitute by multiplying a number by itself. For single-digit numbers, we tin can use multiplication tables to observe the square, while in the case of two or more than than two-digit numbers, we perform multiplication of the number past itself to get the reply. For case, 9 × 9 = 81, where 81 is the square of 9. Similarly, 3 × 3 = 9, where 9 is the square of 3.
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Square Root of Numbers
| Square Root of 1 | Square Root of 2 |
| Foursquare Root of 3 | Square Root of iv |
| Square Root of 5 | Square Root of half-dozen |
| Square Root of vii | Foursquare Root of viii |
| Square Root of 9 | Square Root of ten |
| Square Root of 12 | Square Root of 13 |
| Foursquare Root of fifteen | Foursquare Root of sixteen |
| Foursquare Root of 17 | Square Root of 18 |
| Square Root of 20 | Square Root of 24 |
| Foursquare Root of 25 | Square Root of 32 |
| Square Root of 36 | Foursquare Root of xl |
| Foursquare Root of 45 | Square Root of 48 |
| Square Root of 49 | Square Root of 50 |
| Square Root of 64 | Square Root of 72 |
| Square Root of lxxx | Square Root of 81 |
| Square Root of 100 | Square Root of 121 |
| Foursquare Root of 125 | Square Root of 144 |
| Square Root of 169 | Square Root of 196 |
| Square Root of 225 | Square Root of 256 |
| Square Root of 289 | Square Root of 400 |
Examples on Square Root
-
Instance i: Observe out the square root of 529 by the prime factorization method.
Solution:
Prime factorization of 529.
We can meet that, 529 = 23×23 ⇒ √529= 23
∴ √529= 23.
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Practise Questions on Foursquare Root
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FAQs on Square Root
What is Square Root in Math?
The square root of a number is that gene of a number which when multiplied past itself gives the original number. For example, 2 is the square root of iv, and this is expressed as √4 = 2. This means when two is multiplied by 2 it results in iv and this tin be verified equally two × ii = 4.
☛ Bank check:
- Square Root one to ten
- Square Root 1 to 20
- Square Root one to 25
- Square Root one to 30
- Foursquare Root 1 to 50
- Foursquare Root 1 to 100
How to Find the Square Root of a Number?
It is very piece of cake to find the foursquare root of a number that is a perfect square. For example, 9 is a perfect foursquare, nine = 3 × three. So, 3 is the square root of 9 and this can be expressed as √9 = 3.
The square root of a number can be found by using any of the four methods given below:
- Repeated Subtraction Method
- Prime number Factorization Method
- Interpretation and Approximation Method
- Long Division Method
How to Find the Square Root of a Decimal Number?
The square root of a decimal number can be institute by using the estimation method or the long division method. In the case of decimal numbers, we make pairs of whole number parts and fractional parts separately. And so, we comport out the process of long segmentation in the same fashion as any other whole number.
Can Square Root be Negative?
Yes, the square root of a number can exist negative. In fact, all the perfect squares similar 4, ix, 25, 36, etc have 2 square roots, one is a positive value and ane is a negative value. For example, the square roots of 4 are -2 and 2. To verify this, nosotros can run into that (-2) × (-2) = 4. Similarly, the square roots of 9 are 3 and -3.
What is the Square Root Symbol?
The symbol that is used to denote square root is called the radical sign '√ '. The term written inside the radical sign is called the radicand.
What is the Formula for Calculating the Foursquare Root of a Number?
The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 equally its exponent, it means we need to notice the square root of the number.
What is the Square and Foursquare Root of a Number?
The square of a number is the product that we become on multiplying a number by itself. For instance, 6 × 6 = 36. Here, 36 is the square of 6. The square root of a number is that cistron of a number which when multiplied by itself gives the original number. Now, if we want to discover the foursquare root of 36, that is, √36, nosotros get the answer equally, √36 = half dozen. Hence, we tin meet that the square and the square root of a number are changed operations of each other.
Which Method is Used to Notice the Square Root of Not-Perfect Square Numbers?
In Math, a non-perfect or an imperfect square number is considered as a number that is in decimal form. The square root of a non-perfect foursquare number can be calculated by using the long partitioning method.
How to Find a Square Root on a Calculator?
To detect the foursquare root value of whatsoever number on a calculator, we simply need to type the number for which we want the square root and then insert the square root symbol √ in the calculator. For example, if we need to find the foursquare root of 81, we should type 81 in the estimator and and then printing the symbol √ to get its square root. We will become √81 = nine.
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- Fraction Square Root Calculator
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- Simplify Square Roots Calculator
How to Multiply Ii Square Root Values Together?
Let us say we take two numbers a and b. First, we will discover the square root of the numbers a and b. And then, after finding the foursquare root we will multiply the square roots value together. Let us understand this with a practical analogy. For example, multiply √four × √16. The square root of 4 is two (√4 = 2) and the foursquare root of 16 is four (√sixteen = four). Now, we will multiply the value of the square root of four and sixteen, i.e., two × 4 = 8.
What are the Applications of the Foursquare Root Formula?
At that place are diverse applications of the square root formula:
- Square root formula is mainly used in algebra and geometry. Information technology helps in finding the roots of a quadratic equation.
- We can easily calculate the area, volume, and other measurements using the square root formula.
- It is widely used by engineers.
What does the Square of a Number mean?
The product that we become on multiplying a number by itself is the foursquare of the number. For example, 5 × 5 = 25. Here, 25 is the foursquare of 5 and this tin also exist written every bit 5ii = 25.
Why is the Square of a Negative Number Positive?
The square of a negative number is positive because when two negative numbers are multiplied it always results in a positive number. For instance, (-4) × (-4) = 16.
Source: https://www.cuemath.com/algebra/squares-and-square-roots/
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