Question

$\large\boxed{\textsf{\textbf{\blue{QUESTION\::-}}}}$
find which of the following number is a perfect square
a) 576
b) 11025​

Answer 1

Answer:

(i) Given 576 A perfect square can always be expressed as a product of pairs of equal factors.Now resolve 576 into prime factors, we get 576 = 64 X 9

= 8 X 8 X 3 X 3

= 8 X 3 X 8 X 3

= 24 X 24

= (24)2

Hence, 24 is the number whose square is 576

∴ 576 is a perfect square

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(ii) Given 11025 A perfect square can always be expressed as a product of pairs of equal factors.Now resolve 11025 into prime factors, we get 11025 = 441 X 25

= 49 X 9

= 7 X 7 X 3 X 3 X 5 X 5

= 7 X 3 X 5 X 7 X 3 X 5

= 105 X 105

= (105)2

Hence, 105 is the number whose square is 11025

∴ 11025 is a perfect square.

Answer 2

Answer:

$\large\boxed{\textsf{\textbf{\blue{QUESTION\::-}}}}$

find which of the following number is a perfect square

a) 576

b) 11025

$\large\boxed{\textsf{\textbf{\blue{SOLUTION\::-}}}}$

a) 576

In order to find if the given number is a perfect square,

At first,

We’ll resolve the given number into prime factors:

Hence,

576 = 64 × 9

= 8 × 8 × 3 × 3

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

= (2 × 2 × 2 × 3) × (2 × 2 × 2 × 3)

= 24 × 24

= (24)2

Hence, it is a perfect square.

b) 11025

In order to find if the given number is a perfect square,

At first,

We’ll resolve the given number into prime factors:

Hence,

11025 = 441 × 25

= 49 × 9 × 5 × 5

= 7 × 7 × 3 × 3 × 3 × 3 × 5 × 5

= (7 × 5 × 3 × 3) × (7 × 5 × 3 × 3)

= 315 × 315

= (315)2

Hence,

It is a perfect square.

Step-by-step explanation:

I hope it helps!!...