Question

Chứng minh rằng:\(\sqrt{52+12\sqrt{10}}-\sqrt{47-6\sqrt{10}}=3\sqrt{2}\)

Answer 1

mình sửa lại đề vì đề sai

\(\sqrt{53+12\sqrt{10}}-\sqrt{47-6\sqrt{10}}=\sqrt{53+2\sqrt{360}}-\sqrt{47-2\sqrt{90}}=\sqrt{45+2\sqrt{45}\sqrt{8}+8}-\sqrt{45-2\sqrt{45}\sqrt{2}+2}=\sqrt{45}+2\sqrt{2}-\sqrt{45}+\sqrt{2}=3\sqrt{2}\)

Answer 2

√ 53 + 12 √ 10 − √ 47 − 6 √ 10 = √ 53 + 2 √ 360 − √ 47 − 2 √ 90 = √ 45 + 2 √ 45 √ 8 + 8 − √ 45 − 2 √ 45 √ 2 + 2 = √ 45 + 2 √ 2 − √ 45 + √ 2 = 3 √ 2