Question

find the smallest number by which each of following number must be multiplied to obtain a perfect square 768 and 252​

Answer 1

Answer:

LCM of 768

$\sqrt{768 } = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3}$We must multiply by 3 on both side to get a perfect square

$\sqrt{768 \times 3} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3}$

$\sqrt{2304} = \sqrt{2 \times 2 \times 2 \times 2 \times 3}$

$\sqrt{2304} = 48$