Q6 of 50 Page 6

Which of the following triplets are Pythagorean?
(i) (1, 2, 3) (ii) (3, 4, 5) (iii) (6, 8, 10)
[We know that the three natural numbers m, n, p are said to be Pythagorean triplets if m2 + n2 = p2.]

(i) 12 + 22 = 1 + 4 = 5 ¹ 32
(ii) 32 + 42 = 9 + 16 = 25 = 52
(iii) 62 + 82 = 36 + 64 = 100 = 102
Therefore, (3, 4, 5) and (6, 8, 10) are Pythagorean triplets.

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4 Write down the correct number in the box: [For every natural number n, we have
(n + 1)2 - n2 = (n + 1 - n)(n + 1 + n) = (n + 1) + n.]
(a) 232 - 222 = ________
(b) 1012 -1002 = _________
(c) 5512 - 5502 = __________ 5 Write down the correct number in each box:
(a) 652 = 6 x 7(100) + 52 = 4200 + 25 =_________
(b) 752 = 7 x 8(100) + 52 = 5600 + 25 =__________ 7 Which of the following triplets are Pythagorean?
(i) (1, 1, 1) (ii) (2, 2, 3)
[We know that the three natural numbers m, n, p are said to be Pythagorean triplets if m2 + n2 = p2.] 8 Observe a pattern in the following and find the missing numbers:
222
121 = _______
1+2+1
(333)2
12321 =_________
1+2+3+2+1
1234321 =__________
123454321 =__________
12345654321 =__________
1234567654321 =__________
123456787654321=___________
(999999999)2
12345678987654321 = ___________________________________
1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1