Question

What is the square root of 225As I am new to thisPlease answer step by step in the easiest form possible

Answer 1

Given:

$225$

To Determine: The square root of the given number

Solution

Step 1: Express 225 as the product pf its prime factors of 225

$\begin{gathered} 225=3\times3\times5\times5 \\ 225=3^2\times5^2 \end{gathered}$

Step 2: Separate the factors into their own square root

$\begin{gathered} \sqrt{225}=\sqrt{3^2\times5^2} \\ \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \end{gathered}$

Step 3: Solve the individual's squares

$\begin{gathered} \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \\ \sqrt{225}=3\times5=15 \end{gathered}$

Hence, the square root of 225 is 15