Question

Find the square root of 1764 by the prime factorization method.

Answer 1

Hint: To find the square root of the given number through the prime factorization method we need to first divide the given number into its prime factor and then make the pair of similar factors such that the both factors in each pair are equal. And then after taking one factor from the pair. and finally find the product of factors obtained by taking one factor from each pair. That product is the square root of the given number.

Complete step-by-step answer:
In this question, we need to find the square root of 1764.
First, we make the prime factor of 1764.
1764 = 2 x 2 x 3 x 3 x 7 x 7.

Now, making pairs
1764 = 2 x 2 x 3 x 3 x 7 x 7

Take one factor from each pair
So, in this case we get 2, 3 and 7.
And find the product.
$ \Rightarrow $ 2 x 3 x 7 = 42

This product is the square root of the given number.
Therefore, $\sqrt {{\text{1764}}} $= $42$.

Note: In finding the square root by prime factorization method, you should know how to find the prime factor of a number. If a number is a perfect square then it means that its square root is a natural number or a rational number or we can say that the number can be written in the form of square of some number i.e. N =${{\text{a}}^2}$. Here the ‘a’ is the square root of number N.