What is Square Root of 6084

• Square root of 6084 is written as $\sqrt{6084}$ (Radical form).
• Square root of 6084 = $\sqrt{6084}$ = $\sqrt{78 \times 78}$ = 78
• In the exponential form, the square root of 625 is expressed as $(6084)^\frac{1}{2}$.

We will now calculate the square root of 6084 by prime factorization or long division method.

Square Root of 6084 By Prime Factorization Method

• Step 1: Prime factors of 6084: 2 x 2 x 3 x 3 x 13 x 13
• Step 2: Prime factors of 6084 in pairs: (2 x 2) x (3 x 3) x (13 x 13)
• Step 3: Now square root of 6084:

$\sqrt{6084} = \sqrt{(2 \times 2) \times (3 \times 3) \times (13 \times 13)}$

$\sqrt{6084} = \sqrt{ 2^2 \times3^2 \times13^2}$

$\sqrt{6084} = \sqrt{(2\times3\times13)^2}$

$\sqrt{6084} = \sqrt{78^2}$

$\sqrt{6084} = 78$

Therefore, the square root of 6084 is ±78

Square Root by Long Division Method

The square root of 6084 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 6084 by putting a bar above 84, 60.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 60. This will be 7 obviously, so place 7 in the quotient and the divisor place which will result in the remainder being 11. 
• Step 3: Drag down 84 beside the remainder 11. Also, add the divisor to itself and write it below.(7 + 7 = 14)
• Step 4: Find a number X such that 14X × X results in a number less than or equal to 1184. The number 8 fits here so fill it next to 14 in the divisor as well as next to 7 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.