Question

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we square root of 529 by long division.
Q.2. Evaluate by using identity :- (1) 79 x 81
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Answer 1

Step-by-step explanation:

1. Step 1 : We write 529 as 5

29

by grouping the numbers in pairs, starting from the right end. (i.e. from the units place ).

Step 2 : Find the number whose square is less than (or equal to) 5. Here it is 2.

Step 3 : Put 2 on the top, and also write 2 as a divisor as shown.

Step 4 : Multiply 2 on the top with the divisor 2 and write 4 under 5 and subtract. The remainder is 1.

Step 5 : Bring down the pair 29 by the side of the remainder 1, yielding 129.

Step 6 : Double 2 and take the resulting number 4. Find that number n such that 4n×n is just less than or equal to 129.

For example: 42×2=84; and 43×3=129 and so n=3.

Step 7 : Write 43 as the next divisor and put 3 on the top along with 2. Write the product 43×3=129 under 129 and subtract. Since the remainder is 0, the division is complete. Hence

√529=23

2. 79×81

= (80-1)(80+1)

= 80^2-1^2

=6400-1

= 6389

Answer 2

Step-by-step explanation:

Q2:

$79 \times 81 = (80 - 1) \: (80 + 1) \\ (x - y) \: (x + y) = {x}^{2} - {y}^{2} \\ (80 - 1) \: (80 + 1) = {(80)}^{2} - {(1)}^{2} \\ = 6400 - 1 \\ = 6399$

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