Find the smallest number by which 640 must be multiplied so that the product becomes a perfect square. Also, find the square root of the resulting number.
Show answer & explanation
Correct answer: D
Explanation
Given:
Number = 640
For a number to be a perfect square, the exponents of its prime factors must be even.
640 = 64 × 10 = 2⁶ × (2 × 5) = 2⁷ × 5
2⁷ × 5 ⇒ The exponent of 2 is odd, and the exponent of 5 is also odd.
To make this a perfect square, we must multiply it by 2 × 5 = 10.
640 × 10 = 6400
√6400 = 80
Multiplying by 10 transforms 640 into the perfect square 6400, and its square root is 80.