Question

Find the square root of 2025.

Answer 1

Hint: Square of any number A means we have to evaluate ${\left( A \right)^{\dfrac{1}{2}}}$. Use this concept along with basic factorization techniques on the given number whose square is to be found, to get the answer.

Complete step-by-step answer:
Given number is 2025.
Now we have to find out the square root of this number.
i.e. $\sqrt {2025} $ .
This is also written as ${\left( {2025} \right)^{\dfrac{1}{2}}}$……… (1)
So first factorize the given number,
$ \Rightarrow 2025 = 5 \times 5 \times 3 \times 3 \times 3 \times 3 = \left( {{5^2}} \right)\left( {{3^4}} \right)$
So substitute this value in equation (1) we have,
$ \Rightarrow {\left( {2025} \right)^{\dfrac{1}{2}}} = {\left( {\left( {{5^2}} \right)\left( {{3^4}} \right)} \right)^{\dfrac{1}{2}}} = \left( {{5^{2 \times \dfrac{1}{2}}}} \right)\left( {{3^{4 \times \dfrac{1}{2}}}} \right) = 5\left( {{3^2}} \right) = 5\left( 9 \right) = 45$.
So the required square root of 2025 is 45.
So this is the required answer.

Note: Factorization is the method of obtaining all the factors of the given number. The factors which are repeating add to the power eventually and thus square root can be obtained. Use these concepts to get on the right track for solving problems of this kind.