### Prime factorisation and square roots

Finding the prime factors of a number can help us to determine whether the number is a perfect square and if it is, to find the square root of such a number.

#### Example

Find the square root of 2025 by finding the prime factors of 2025.

#### Solution

We can write:

\begin{align}2025&=3×3×3×3×5×5\\\\
&=(3×3×5)×(3×3×5)\\\\
&=(3×3×5)^2\end{align}

so 2025 is a square number and:

\begin{align}\sqrt{2025}&=3^2×5\\\\ &=45\end{align}### Summary

- A number multiplied by itself is called the square of the original number.
- The square root of a number is the number that when multiplied by itself gives the original number.
- The product of the square is equal to the square of the product.
- The square root of a product of square numbers is the product of the square roots of the original numbers.