What is Square Root of 361

• Square root of 361 is written as $\sqrt{361}$ (Radical form).
• Square root of 361 = $\sqrt{361}$ = $\sqrt{19 \times 19}$ = 19
• In the exponential form, the square root of 625 is expressed as $(361)^\frac{1}{2}$.

We will now calculate the square root of 361 by prima factorization or long division method.

Square Root of 361 By Prime Factorization Method

• Step 1: Prime factors of 361: 19 x 19
• Step 2: Prime factors of 361 in pairs: (19 x 19)
• Step 3: Now the square root of 361:

$\sqrt{361} = \sqrt{(19 \times 19)}$

$\sqrt{361} = \sqrt{ 19^2}$

$\sqrt{361} = 19$

Therefore, the square root of 361 is ±19

Square Root by Long Division Method

The square root of 361 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 361 by putting a bar above 61, 3.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 3. This will be 1 obviously, so place 1 in the quotient and the divisor place which will result in the remainder being 2. 
• Step 3: Drag down 61 beside the remainder 2. 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 261. The number 9 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.