What is Square Root of 400

• Square root of 400 is written as $\sqrt{400}$ (Radical form).
• Square root of 400 = $\sqrt{400}$ = $\sqrt{20 \times 20}$ = 20
• In the exponential form, the square root of 625 is expressed as $(400)^\frac{1}{2}$.

We will now calculate the square root of 400 by prime factorization or long division method.

Square Root of 400 By Prime Factorization Method

• Step 1: Prime factors of 400: 2 x 2 x 2 x 2 x 5 x 5
• Step 2: Prime factors of 400 in pairs: (2 x 2) x (2 x 2) x (5 x 5)
• Step 3: Now square root of 400:

$\sqrt{400} = \sqrt{(2 \times 2) \times (2 \times 2) \times (5 \times 5)}$

$\sqrt{400} = \sqrt{ 2^2 \times2^2 \times5^2}$

$\sqrt{400} = \sqrt{(2\times2\times5)^2}$

$\sqrt{400} = \sqrt{20^2}$

$\sqrt{400} = 20$

Therefore, the square root of 400 is ±20

Square Root by Long Division Method

The square root of 400 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 400 by putting a bar above 00, 4.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 4. This will be 2 obviously, so place 2 in the quotient and the divisor place which will result in the remainder being 0. 
• Step 3: Drag down 00 beside the remainder 0. Also, add the divisor to itself and write it below.(2 + 2 = 4)
• Step 4: Find a number X such that 4X × X results in a number less than or equal to 0. The number 0 fits here so fill it next to 4 in the divisor as well as next to 2 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.