The square root of 576 is ____.

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Detailed Solution

The square root of 576 is 24.
The given number is 576.
Overline every pair of digits starting from the digit at one’s place. For the numbers having odd digits, the starting digits will also have the overline.
Here, the number of digits is odd. After putting the bar, the number becomes

5 ¯ 76 ¯ .

Now, determine the number having squares equal to or less than the digits under the first overline.
We have

22 < 5 < 32 .

So, 2 is the largest number whose square is less than 5.
This number is the divisor and quotient it with the number under the first overline as the dividend. Divide and get the remainder. So, the divisor is 2 and the dividend is 5. Then,
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So, the remainder is 1.
Now, transfer the number under the next overline to the right of the remainder i.e., bring 76 to the right of 1.
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Now, the new dividend is 176.
Then, the new divisor should be double of the previous one. Add a blank to the right of it. The double of the divisor 2 is 4.
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Locate the digit to complete the number. To ensure that the result of multiplying the new divisor by the new quotient is less than or equal to the dividend, fill in the blank with the largest digit you can think of. This digit will also become the new digit in the quotient.
In this case,