Question

by which number 675is to be multiplied so that the product is a perfect square also find the square root of the product​

Answer 1

First, we'll prime factorize 675.

$\begin{array}{c|c} \tt 3 & \sf{675} \\ \cline{1-2} \tt 3 & \sf 225\\ \cline{1-2} \tt 3 & \sf 75 \\ \cline{1-2} \tt 5 & \sf 25 \\ \cline{1-2} & \sf 5\\ } \endarray$

675 → 3 × 3 × 3 × 5 × 5

Now, pair the prime factors of the number obtained.

675 → 3 × 3 × 3 × 5 × 5

675 → (3 × 3) × 3 × (5 × 5)

Since, '3' doesn't have a pair, 675 is not a perfect square.

∴ We need to multiply '3' to 675 to obtain a perfect square.

675 × 3 → (3 × 3) × (3 × 3) × (5 × 5)

2025 → (3 × 3) × (3 × 3) × (5 × 5)

Now, take one number from each pair and multiply them to get the square root.

√2025 = 3 × 3 × 5

√2025 = 9 × 5

√2025 = 45

∴ The square root of the product obtained is 45.

Answer 2

Answer:

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