Question

.Are the following numbers perfect squares? Give reasons,(a) 729000 (b) 5398(c) 1024 (d) 52900A 2116(8) 5929(e) 97297​

Answer 1

_______Solution________

(a) 729000

• 729000 = 2×2×2×3×3×3×5×5×5
• 729000 = 2²×3²×5² × 2× 3 × 5

Here, Prime factor's of 729000 is not in pair. So it is not a perfect Square.

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(b) 5398

• 5398 = 2 × 2699

Here, Prime factor's of 5398 is not in pair. So it is not a perfect Square .

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(c) 1024

• 1024 = 2×2×2×2×2×2×2×2×2×2
• 1024 = 2²×2²×2²×2²×2²

Here, Prime factor's of 1024 is in pair. So it is a perfect Square .

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(d) 52900

• 52900 = 2×2×5×5×23×23
• 52900 = 2²×5²×23²

Here, Prime factor's of 52900 is in pair. So it is a perfect Square .

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(e) 2116

• 2116 = 2×2×23×23
• 2116 = 2² × 23²

Here, Prime factor's of 2116 is in pair. So it is a perfect Square .

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(f) 5929

• 5929 = 7×7×11×11
• 5929 = 7² × 11²

Here, Prime factor's of 5929 is in pair. So it is a perfect Square .

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(g) 97297

• 97297 is ending with 7 hence can not be a perfect Square .

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Answer 2

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Are the following numbers perfect squares?

• (a) 729000::-its not a perfect square
• (b) 5398::'its not a perfect square
• (c) 1024::- Yes its a perfect square.
• (d) 52900::- Yes its a perfect square.
• (E) 2116::- Yes its a perfect square.
• (8) 5929::- Yes its a perfect square.
• (e) 97297::- its not a perfect square

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