根号下5+2倍根号6加根号下7–4倍根号3–根号下6–4倍根号2等于多少,参考答案我看不懂.

Question

根号下5+2倍根号6加根号下7–4倍根号3–根号下6–4倍根号2等于多少,参考答案我看不懂.

Answer 1

√(5+2√6)=√[(√3)²+2√3×√2+(√2)²]=√(√3+√2)²=√3+√2
√(7-4√3)=√[2²-2×2×√3+(√3)²]=√(2-√3)²=2-√3
√(6-4√2)=√[2²-2×2×√2+(√2)²]=√(2-√2)²=2-√2
∴√(5+2√6)+√(7-4√3)-√(6-4√2)
=√3+√2+2-√3-(2-√2)
=√2+2-2+√2
=2√2