Question

Find the square root of the following by long division (1-4)
1. 961
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Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Answer :}} }} }$

• √961 = 31

$\underline{ \underline{ \Large \pmb{\sf { {Clarification :}} }} }$

• Here, firstly we set the number in the form of a long division and marked off the digits in pairs from right to left by placing bar on every pair. (only 1 pair is formed).

• Then, we considered the digit at extreme left. It is 9. We found the largest number whose square is closest to this "9". We got the number as 3. So, we wrote it on the top in the quotient's place We didn't get any remainder.

• After that, we brought down the next pair, i.e., 61 and doubled the first divisor 3 and wrote it as next divisor.

• Doubling the first divisor we get the second divisor as 6.

• Then, we divided 6 into 6, we got 1. We wrote 1 on the top in the quotient's place as well as to the right of the divisor 6.

• We multiplied 61 by 1 and subtracted the product from 61. The remainder is 0.So, the square root of 961 is 31.

$\underline{ \underline{ \Large \pmb{\sf { {Verification :}} }} }$

Let's check whether 961 is the square of 31 or not.

→ √961 = 31

→ 961 = (31)²

→ 961 = (30 + 1)²

→ 961 = (30)² + 2( 30 × 1 ) + (1)²

→ 961 = 900 + 60 + 1

→ 961 = 961

LHS = RHS

Hence, verified!!