What is Square Root of 729

• Square root of 729 is written as $\sqrt{729}$ (Radical form).
• Square root of 729 = $\sqrt{729}$ = $\sqrt{27 \times 27}$ = 27
• In the exponential form, the square root of 625 is expressed as $(729)^\frac{1}{2}$.

We will now calculate the square root of 729 by prime factorization or long division method.

Square Root of 729 By Prime Factorization Method

• Step 1: Prime factors of 729: 3 x 3 x 3 x 3 x 3 x 3
• Step 2: Prime factors of 729 in pairs: (3 x 3) x (3 x 3) x (3 x 3)
• Step 3: Now square root of 729:

$\sqrt{729} = \sqrt{(3 \times 3) \times (3 \times 3) \times (3 \times 3)}$

$\sqrt{729} = \sqrt{ 3^2 \times3^2 \times3^2}$

$\sqrt{729} = \sqrt{(3\times3\times3)^2}$

$\sqrt{729} = \sqrt{27^2}$

$\sqrt{729} = 27$

Therefore, the square root of 729 is ±27

Square Root by Long Division Method

The square root of 729 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 729 by putting a bar above 29, 7.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 7. This will be 2 obviously, so place 2 in the quotient and the divisor place which will result in the remainder being 3. 
• Step 3: Drag down 29 beside the remainder 3. Also, add the divisor to itself and write it below.(2 + 2 = 4)
• Step 4: Find a number X such that 4X × X results in a number less than or equal to 329. The number 7 fits here so fill it next to 4 in the divisor as well as next to 2 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.