What is Square Root of 225

• Square root of 225 is written as $\sqrt{225}$ (Radical form).
• Square root of 225 = $\sqrt{225}$ = $\sqrt{15 \times 15}$ = 15
• In the exponential form, the square root of 625 is expressed as $(225)^\frac{1}{2}$.

We will now calculate the square root of 225 by prime factorization or long division method.

Square Root of 225 By Prime Factorization Method

• Step 1: Prime factors of 225: 3 x 3 x 5 x 5
• Step 2: Prime factors of 225 in pairs: (3 x 3) x (5 x 5)
• Step 3: Now square root of 225:

$\sqrt{225} = \sqrt{(3 \times 3) \times (5 \times 5)}$

$\sqrt{225} = \sqrt{ 3^2 \times5^2}$

$\sqrt{225} = \sqrt{(3\times5)^2}$

$\sqrt{225} = \sqrt{15^2}$

$\sqrt{225} = 15$

Therefore, the square root of 225 is ±15

Square Root by Long Division Method

The square root of 225 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 225 by putting a bar above 25, 2.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 2. This will be 1 obviously, so place 1 in the quotient and the divisor place which will result in the remainder being 1. 
• Step 3: Drag down 25 beside the remainder 1. Also, add the divisor to itself and write it below.(1 + 1 = 2)
• Step 4: Find a number X such that 2X × X results in a number less than or equal to 125. The number 5 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient.
• Step 5: Find the remainder and now drag down the next pair from the dividend. Check the following animation that outlines all the steps.