What is Square Root of 289

• Square root of 289 is written as $\sqrt{289}$ (Radical form).
• Square root of 289 = $\sqrt{289}$ = $\sqrt{17 \times 17}$ = 17
• In the exponential form, the square root of 625 is expressed as $(289)^\frac{1}{2}$.

We will now calculate the square root of 289 by prima factorization or long division method.

Square Root of 289 By Prime Factorization Method

• Step 1: Prime factors of 289: 17 x 17
• Step 2: Prime factors of 289 in pairs: (17 x 17)
• Step 3: Now the square root of 289:

$\sqrt{289} = \sqrt{(17 \times 17)}$

$\sqrt{289} = \sqrt{ 17^2}$

$\sqrt{289} = 17$

Therefore, the square root of 289 is ±17

Square Root by Long Division Method

The square root of 289 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 289 by putting a bar above 89, 2.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 2. This will be 1 obviously, so place 1 in the quotient and the divisor place which will result in the remainder being 1. 
• Step 3: Drag down 89 beside the remainder 1. 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 189. The number 7 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.