Show that 500 is not a perfect square- - Maths Q-A

We have to show that 500 is not a perfect squareOn prime factorisation of 500, we get500=2 × 2 × 5 × 5 × 5On grouping the factors into pairs,500=)2× 2×)5× 5 ...

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Standard VII

Mathematics

Writing a Number as a Product of Its Primes (Power Rotation)

Show that 500...

Question

Show that $500$ is not a perfect square.

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Solution

We have to show that $500$ is not a perfect square
On prime factorisation of $500$ , we get
$500 = 2 \times 2 \times 5 \times 5 \times 5$
On grouping the factors into pairs,
$500 = 2 \times 2 \times 5 \times 5 \times 5$
Any number is a perfect square when all of its prime factors are paired. Here, $5$ is left unpaired.
Therefore, $500$ is not a perfect square.

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Show that 500 is not a perfect square.

We have to show that 500 is not a perfect squareOn prime factorisation of 500, we get500=2×2×5×5×5On grouping the factors into pairs,500=2×2×5×5×5Any number is a perfect square when all of its prime factors are paired. Here, 5 is left unpaired. Therefore, 500 is not a perfect square.

Show that $500$ is not a perfect square.