Question

Let us prove that root 108-root 75=root 3​

Answer 1

Answer: prove that root 108-root 75=root 3

Answer 2

$LHS \: = \: \sqrt{108} \: - \: \sqrt{75} \\ = \sqrt{2 \times 2 \times 3 \times 3 \times 3} \: - \: \sqrt{5 \times 5 \times 3} \\ = 2 \times 3 \sqrt{3 } \: - \: 5 \sqrt{3} \\ = 6 \sqrt{3} \: - \: 5 \sqrt{3} \\ = \sqrt{3}$

$RHS \: = \: \sqrt{3}$

.·.$LHS = RHS \: (proved)$