Which of the following number are perfect square? $(a).\ 81\ \ (b).\ 168\ \ (c).\ 196\ \ (d).\ 14400\ \ (e).\ \ 625\ \ (f).\ 570$

Given: $(a).\ 81\ \ (b).\ 168\ \ (c).\ 196\ \ (d).\ 14400\ \ (e).\ \ 625\ \ (f).\ 570$

To do: To find the perfect square among the given numbers.

Solution:

$(a).\ 81$

On factorizing $81$:

$81=3\times3\times3\times3=9^2$

Thus, $81$ is a perfect square.

$(b).\ 168$

On factorizing $168$:

$168=2\times2\times2\times3\times7=2^3\times3\times7$

Thus, $168$ is not a perfect square.

$(c).\ 196$

On factorizing $196$:

$196=2\times2\times7\times7=2^2\times7^2$

Thus, $196$ is a perfect square.

$(d).\ 14400$

On factorizing $14400$:

$14400=12\times12\times10\times10=12^2\times10^2$

Thus, $14400$ is a perfect square.

$( e).\ 625$

On factorizing $625$

$625=5\times5\times5\times5=5^2\times5^2$

Thus, $625$ is a perfect square.

$(f).\ 570$

On factorizing $570$:

$570=2\times3\times5\times19$

Thus, $570$ is not a perfect square.

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Updated on: 10-Oct-2022

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