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Find the square of the following numbers.

(i) 32

(ii) 35

(iii) 86

(iv) 93

(v) 71

(vi) 46

1) 32

We can find the square using direct multiplication

= 32 x 32 = 1024

But above method can be cumbersome to calculate. We can calculate such values in the another better way f

Since, 32 can be written as (30+2)

So, 32

Now we know the identity

(a+b)

= 30

= 900 + 120 + 4 = 1024

2) (35)

Solving on similar lines as above

= 30

= 900 + 300 + 25 = 1225

3) 86

= 80

= 6400 + 960 + 36 = 7396

4) 93

= 90

= 8100 + 540 + 9 = 8649

5) 71

= 70

= 4900 + 140 + 1 = 5040 + 1 = 5041

6) 46

= 40

= 1600 + 480 + 36 = 2080 + 36 = 2116

Write a Pythagorean triplet whose one member is:

(i) 6

(ii) 14

(iii) 16

(iv) 18

As we know 2n, n

1) If we take n

So we can 2n = 6

Therefore, n = 3

And, n

And,n

Test: 6

Hence, the triplet is 6, 8, and 10 Answer

2) If we take n

So we can take 2n= 14, therefore, n = 7

Now, n

And, n

Test: 14

Hence, the triplet is 14, 48, and 50 Answer

3) If we take n

Let us assume 2n = 16, then n = 8

Now, n

And, n

Test: 16

Hence, the triplet is 16, 63, and 65 Answer

4) If we take n

Let us assume 2n = 18, therefore, n = 9

Now, n

And, n

Test: 18

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