## Book: NCERT - Mathematics

### Chapter: 6. Squares and Square Roots

#### Subject: Maths - Class 8th

##### Q. No. 2 of Exercises 6.2

Listen NCERT Audio Books - Kitabein Ab Bolengi

2
##### Write a Pythagorean triplet whose one member is(i) 6 (ii) 14(iii) 16 (iv) 18

For any natural number m > 1, 2m, m2 - 1, m2+ 1 forms a Pythagorean triplet

(i) If we consider,m2 + 1 = 6, then m2 = 5

The value of m will not be an integer

Now,

If we consider,m2 - 1 = 6, then m2 = 7

Again the value of m is not an integer

Let us take 2m = 6

So, m = 3

Hence, the Pythagorean triplets are:

2 x 3, 32 - 1, 32+ 1 or 6, 8, and 10

(ii) If we considerm2 + 1 = 14, then m2 = 13

The value of m will not be an integer

If we consider m2 - 1 = 14, then m2 = 15

Again the value of m is not an integer

Let 2m = 14

m = 7

Hence, m2 - 1 = 49 - 1 = 48 and m2 + 1 = 49 + 1 = 50

Hence, the required Pythagorean triplet is 14, 48, and 50

(iii) If we considerm2 + 1 = 16, then m2 = 15

The value of m will not be an integer

If we considerm2 - 1= 16, then m2 = 17

Again the value of m is not an integer

Now, let 2m = 16

m = 8

Therefore, m2 - 1 = 64 - 1 = 63 and m2 + 1 = 64 + 1 = 65

Therefore, the Pythagorean triplet is 16, 63, and 65

(iv) If we considerm2 + 1 = 18,

m2 = 17

Then, the value of m will not be an integer

If we considerm2 - 1 = 18, then m2 = 19

Again the value of m is not an integer

So, let 2m =18

m = 9

Thus, m2 - 1 = 81 - 1 = 80 and m2 + 1 = 81 + 1 = 82

Therefore, the Pythagorean triplet is 18, 80, and 82

2

1
2