how to find the square root of a number that isn t a perfect square Let s use the square root of 147 as an example 147 isn t the product of two perfect squares so we can t get an exact integer value as above However it is the product of one perfect square and another number 49 and 3 We can use this information to write our answer in simplest terms as follows Sqrt 147 Sqrt 49 3 Sqrt 49 Sqrt 3
The square root formula is used to find the square root of a number We know the exponent formula n x x n x 1 n When n 2 we call it square root We can use any of the above methods for finding the square root such as prime factorization and so on 9 1 2 9 3 3 3 The prime factorization of 180 is 180 2 2 3 3 5 If we make the pair of the prime factors we see that the prime factor 5 is not in the pair Therefore 180 is not a perfect square and hence the square root is not perfect The square root of 180 180 2 3 5 6 5 Division Method
how to find the square root of a number that isn t a perfect square
how to find the square root of a number that isn t a perfect square
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The method to find the square root of any number is easy if the given number is a perfect square We can determine the square root of perfect squares by prime factorisation method But if the number is not a perfect square then it is difficult to find the square root of it Math Article How To Find Square Root Of A Number A square has the same length and width Which means if the length is equal to 3 then the width should also be equal to 3 Therefore the area of square will be l b i e 3 3 9 It can also be written as 3 2 or called as 3 squared or 3 to the 2 nd power
Supporting Lessons Media error Format s not supported or source s not found Download File mathswithmum wp content uploads 2018 10 squarerooto mp4 1 Square Root Calculator Enter a number to calculate its square root Find Square Root Finding Square Roots Interactive Square Root of Numbers that are not Perfect Squares Examples 1 Evaluate 2 correct up to two places of decimal Solution The given number is 2 The square root of 1 is 1 Also the square root of 2 25 is 1 5 The 2 is in between 1 and 2 25 Therefore to find the square root of a 2 add 6 zeros after the decimal point
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If the square root is not a whole number then the given number is not a perfect square For example to check whether 24 is a perfect square or not let us calculate its square root 24 4 89 As we can see 4 89 is not a whole number so 24 Suppose you want sqrt 65 You already know sqrt 64 So you can first graph y sqrt x then draw a tangent at x 64 Find the equation of the tangent and substitute for x 65 As the tangent approximates the square root function you ll get an rough approximation of sqrt 65
Solved Examples Practice Problems Frequently Asked Questions What Are Square and Square Roots When you multiply a number by itself you get the square of a number For instance 3 3 9 So the square of 3 is 9 Square root goes the other way round If the square of 3 is 9 then the square root of 9 is 3 If a number is a perfect square number then there exists a perfect square root If a number ends with an even number of zeros 0 s then it can have a square root The two square root values can be multiplied For example 3 can be multiplied by 2 then the result should be 6
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how to find the square root of a number that isn t a perfect square - To check the perfectness of your square you can simply calculate the square root of a given number If the square root is an integer your number is the perfect square Let s calculate the squares of the following numbers 49 and 53 49 7 7 is an integer number 49 is a perfect square