Question

find the square root of 196 by using prime factorization method

Answer 1

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Answer 2

The question is to find the square root of 196 by using the prime factorization method

The solution to this problem is we have to find the square root of the given number by the prime factorisation method.

The prime factorisation method is used to find the factors of a given number.

we can also find the LCM and HCF of the numbers using a prime factorization method.

The prime factorisation of the number 196 is

$2)196 \\ 2)98 \\ 7)49 \\ 7)1$

The prime factors of the given number are

${2}^{2} \times {7}^{2}$

On taking the square root for the given factors we get the values as

$\sqrt{ {2}^{2} \times {7}^{2} }$

The square and the root will get cancelled and we get the values as

$2 \times 7 = 14$

Therefore, the square root of the given number is 14.

let's verify the answer

$14 \times 14 = 196$

Hence verified.

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