Find the square root of 60.84 by using with divis

To find the square root of 60.84 using the division method, follow these steps:

Step 1: Prepare the Number

First, express 60.84 in a suitable format. We can treat it as 6084 by moving the decimal point two places to the right. This will help in simplifying the calculation.

Step 2: Group the Digits

Next, group the digits in pairs starting from the decimal point. For 6084, we have:

• 60 | 84

Step 3: Find the Largest Square

Now, find the largest square number less than or equal to the first group (60). The largest square is 49 (7 x 7).

Write 7 above the line as the first digit of the square root:

• 7

Step 4: Subtract and Bring Down

Subtract 49 from 60, which gives you 11. Then, bring down the next pair (84) to make it 1184.

Step 5: Double the Quotient

Double the number above the line (7 x 2 = 14) and write it down with a blank space next to it:

• 14_

Step 6: Find the Next Digit

Now, find a digit (let's call it x) such that (140 + x) x is less than or equal to 1184. Testing with x = 8:

• (148) x 8 = 1184

So, x = 8 is correct. Write 8 above the line:

• 7.8

Step 7: Final Result

The square root of 60.84 is approximately 7.8.