Question

14) Without doing any calculation, find the numbers which are surely not perfect squares,
a) 408
b) 257
15)Write a Pythagorean Triplet whose one member is:
a) 16
b) 18
SECTION-C
(4x3=12)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

14) None of them are perfect squares.

15)

a) 65, 63 & 16.

b) 82, 80 & 18.

Step-by-step explanation:

14)

Numbers with digits 2, 3, 7 or 8 at the last digit are not perfect squares, so 408 and 257 are surely not perfect squares. {As they have 8 and 7 at the last digit respectively.}

15)

a)

One of the member: 16.

Let 2n = 16.

→n = 16/2

→n = 8.

Other two members:

${n}^{2} + 1$

${8}^{2} + 1$

$64 + 1$

$65$

${n}^{2} - 1$

${8}^{2} - 1$

$64 - 1$

$63$

Triplet: 8, 63 & 65.

b)

One of the member: 18

Let 2n = 18.

→n = 18/2

→n = 9.

Other members:

${n}^{2} + 1$

${9}^{2} + 1$

$81 + 1$

$82$

${n}^{2} - 1$

${9}^{2} - 1$

$81 - 1$

$80$

Triplet: 82, 80 & 18.

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