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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.


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


We can write:

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

so 2025 is a square number and:

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