Question

二次根式

(根号8/27-5根号3)x根号6+3根号50 (10根号48-6根号27+4根号12)÷根号6 (2根号3+3根号2)平方-(2根号3-3根号2)平方 （根号3-1)(根号3+3) （根号3-2根号2)(2根号3-根号2)

Answer 1

(√8/27-5√3)×√6+3√50
=√(8/27)×√6-5√3×√6+3√(5²×2)
=√(8/27×6)-5√(3×6)+3×5√2
=√(16/9)-5×√(3²×2)+15√2
=4/3-5×3√2+15√2
=4/3-15√2+15√2
=4/3

(10√48-6√27+4√12)÷√6
=10√48÷√6-6√27÷√6+4√12÷√6
=10√(48÷6)-6√(27÷6)+4√(12÷6)
=10√8-6√(9/2)+4√2
=10√(2²×2)-6√(2×3²/2²)+4√2
=20√2-6×3/2×√2+4√2
=20√2-9√2+4√2
=15√2

(2√3+3√2)²-(2√3-3√2)²
=(2√3+3√2+2√3-3√2)(2√3+3√2-2√3+3√2)
=4√3×6√2
=24√6

(√3-1)(√3+3)
=√3×√3+√3×3-1×√3-1×3
=3+3√3-√3-3
=2√3

(√3-2√2)(2√3-√2)
=√3×2√3-√3×√2-2√2×2√3+2√2×√2
=3×2-√6-4√6+2×2
=6-5√6+4
=10-5√6