What is Square Root of 144

• Square root of 144 is written as $\sqrt{144}$ (Radical form).
• Square root of 144 = $\sqrt{144}$ = $\sqrt{12 \times 12}$ = 12
• In the exponential form, the square root of 625 is expressed as $(144)^\frac{1}{2}$.

We will now calculate the square root of 144 by prime factorization or long division method.

Square Root of 144 By Prime Factorization Method

• Step 1: Prime factors of 144: 2 x 2 x 2 x 2 x 3 x 3
• Step 2: Prime factors of 144 in pairs: (2 x 2) x (2 x 2) x (3 x 3)
• Step 3: Now square root of 144:

$\sqrt{144} = \sqrt{(2 \times 2) \times (2 \times 2) \times (3 \times 3)}$

$\sqrt{144} = \sqrt{ 2^2 \times2^2 \times3^2}$

$\sqrt{144} = \sqrt{(2\times2\times3)^2}$

$\sqrt{144} = \sqrt{12^2}$

$\sqrt{144} = 12$

Therefore, the square root of 144 is ±12

Square Root by Long Division Method

The square root of 144 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 144 by putting a bar above 44, 1.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 1. This will be 1 obviously, so place 1 in the quotient and the divisor place which will result in the remainder being 0. 
• Step 3: Drag down 44 beside the remainder 0. 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 44. The number 2 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.