Question

Find the square root of 2025.

Answer 1

Hint: We will see the definition of the square and square root. We will write the prime factors of the given number by doing prime factorization. We will be able to see that a set of factors is repeated two times. Then we will take the product of the prime factors in this set. This product of the prime factors in the set is the square root of the given number.

Complete step by step answer:
We say that a number is a square when it is the product of a number with itself. The square root of a number is defined as the value, which when multiplied to itself gives us the number. The given number is 2025. We have to find the square root of the given number, that means we have to find a value, which multiplied to itself will give 2025.
Let us look at the prime factorization of the given number.
 $ \begin{align}
  & 5\left| \!{\underline {\,
  2025 \,}} \right. \\
 & 5\left| \!{\underline {\,
  405 \,}} \right. \\
 & 3\left| \!{\underline {\,
  81 \,}} \right. \\
 & 3\left| \!{\underline {\,
  27 \,}} \right. \\
 & 3\left| \!{\underline {\,
  9 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & \left| \!{\underline {\,
  1 \,}} \right. \\
\end{align} $
We can see that the factors 5,3 and 3 appear two times. The product of these factors is
 $ 5\times 3\times 3=45 $
So we can say that $ 2025=45\times 45 $ . Therefore, the square root of 2025 is 45.

Note:
 There is an alternate method to find the square root of the given number. We know the method 'Sutra Ekadhikena Poorvena' to find the squares of numbers ending in 5. We can use the reverse process of this method to find the square root of 2025. We will split the number in two parts, 20 and 25. We know that 25 is the square of 5. We have to find a number such that its product with the consecutive number is 20. We can see that $ 4\times 5=20 $ . Hence, we can conclude that the square root of 2025 is 45.