Which of the following numbers are perfect squares ?

11, 12, 16, 32, 36, 50, 64, 79, 81, 111, 121

Given :

The given numbers are 11, 12, 16, 32, 36, 50, 64, 79, 81, 111, 121.

To do :

We have to find the perfect squares among given numbers.

Solution:

Perfect Square: A perfect square has each distinct prime factor occurring an even number of times.

$11 = 1 \times 11$

11 is not a perfect square.

$12=2\times2\times3$

12 is not a perfect square.

$16=2\times2\times2\times2$

16 is a perfect square.

$32=2\times2\times2\times2\times2$

32 is not a perfect square.

$36=2\times2\times3\times3$

36 is a perfect square.

$50=2\times5\times5$

50 is not a perfect square.

$64=2\times2\times2\times2\times2\times2$

64 is a perfect square.

$79=1\times79$

79 is not a perfect square.

$81=3\times3\times3\times3$

81 is a perfect square.

$111=3\times37$

111 is not a perfect square.

$121=11\times11$

121 is a perfect square.

Hence, $16, 36, 64, 81$ and $121$ are perfect squares.

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Updated on: 10-Oct-2022

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