What is Square Root of 578

• Square root of 578 is written as $\sqrt{578}$ (Radical form).
• Square root of 578 = $\sqrt{578}$ ≈ $\sqrt{24.04 \times 24.04}$ ≈ 24.04
• In the exponential form, the square root of 578 is expressed as $(578)^\frac{1}{2}$.

We will now calculate the square root of 578 by the Long Division method.

Square Root by Long Division Method

The square root of 578 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits of 578 by putting a bar above 78, 5. We also pair the 0s in decimals in pairs of 2 from left to right. Added 4 decimal places as it is not a perfect square.
• Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 5. This will be 2 obviously, so place 2 in the quotient and the divisor place which will result in the remainder being 1. 
• Step 3: Drag down 78 beside the remainder 1. 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 178. The number 4 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. Repeat this process to get the decimal places you want. Check the following animation that outlines all the steps.