What is Square Root of 256

• Square root of 256 is written as $\sqrt{256}$ (Radical form).
• Square root of 256 = $\sqrt{256}$ = $\sqrt{16 \times 16}$ = 16
• In the exponential form, the square root of 625 is expressed as $(256)^\frac{1}{2}$.

We will now calculate the square root of 256 by prime factorization or long division method.

Square Root of 256 By Prime Factorization Method

• Step 1: Prime factors of 256: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
• Step 2: Prime factors of 256 in pairs: (2 x 2) x (2 x 2) x (2 x 2) x (2 x 2)
• Step 3: Now square root of 256:

$\sqrt{256} = \sqrt{(2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (2 \times 2)}$

$\sqrt{256} = \sqrt{ 2^2 \times2^2 \times2^2 \times2^2}$

$\sqrt{256} = \sqrt{(2\times2\times2\times2)^2}$

$\sqrt{256} = \sqrt{16^2}$

$\sqrt{256} = 16$

Therefore, the square root of 256 is ±16

Square Root by Long Division Method

The square root of 256 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 256 by putting a bar above 56, 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 56 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 156. The number 6 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.