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If a and b are two distinct prime numbers other than 11, which of the following is a perfect square?
11 x axb
121 x axb
11 xa xa xbxb
121 xa xa xbxb
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⇒ 11 is a prime number by itself.
So, it is not a perfect square.
⇒ 12=2×2×3
12
=
2
2
×3
12
=2
3
∴ 12 is not perfect square.
⇒ 16=2×2×2×2×2
16=2
4
16
=2
2
=4
∴ 16 is a perfect square.
⇒ 32=2×2×2×2×2
32=2
5
32
=
2
5
32
=4
2
∴ 32 is not perfect square.
⇒ 36=2×2×3×3
36
=
2
2
×3
2
36
=6
∴ 36 is a perfect square.
⇒ 50=2×5×5
50
=
5
2
×2
50
=5
2
∴ 50 is not perfect square.
⇒ 79 is a prime number.
So, it is not a perfect square.
⇒ 81=3×3×3×3
81
=
3
4
81
=9
∴ 81 is a perfect square.
⇒ 111 is a prime number.
So, it is not a perfect square.
⇒ 121=11×11
121
=
11
2
121
=11
∴ 121 is a perfect square.
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