What is Square Root of 2500

• Square root of 2500 is written as $\sqrt{2500}$ (Radical form).
• Square root of 2500 = $\sqrt{2500}$ = $\sqrt{50 \times 50}$ = 50
• In the exponential form, the square root of 625 is expressed as $(2500)^\frac{1}{2}$.

We will now calculate the square root of 2500 by prime factorization or long division method.

Square Root of 2500 By Prime Factorization Method

• Step 1: Prime factors of 2500: 2 x 2 x 5 x 5 x 5 x 5
• Step 2: Prime factors of 2500 in pairs: (2 x 2) x (5 x 5) x (5 x 5)
• Step 3: Now square root of 2500:

$\sqrt{2500} = \sqrt{(2 \times 2) \times (5 \times 5) \times (5 \times 5)}$

$\sqrt{2500} = \sqrt{ 2^2 \times5^2 \times5^2}$

$\sqrt{2500} = \sqrt{(2\times5\times5)^2}$

$\sqrt{2500} = \sqrt{50^2}$

$\sqrt{2500} = 50$

Therefore, the square root of 2500 is ±50

Square Root by Long Division Method

The square root of 2500 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 2500 by putting a bar above 00, 25.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 25. This will be 5 obviously, so place 5 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.(5 + 5 = 10)
• Step 4: Find a number X such that 10X × X results in a number less than or equal to 0. The number 0 fits here so fill it next to 10 in the divisor as well as next to 5 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.