Question

Using prime factorisation, find the square roots of $11025$

Answer 1

Let us first determine the factors by the method of prime factorization of $11025$

Hence the factors obtained of $11025$$=3\times 3\times 5\times 5\times 7\times 7$

On grouping and pairing the obtained factors we get$=(3\times 3)\times (5\times 5)\times (7\times 7)$

Then, the Square root of $11025=\sqrt{11025}$

$$\begin{gathered} =\sqrt{(3\times 3)\times (5\times 5)\times (7\times 7)} \\ =\sqrt{(3^2\times 5^2\times 7^2)} \\ =3\times 5\times 7 \\ =105 \end{gathered}$$

∴ The Square root of $11025$is $105$.