Question

Упростите выражения:
1) 5√2 - 4√8 + 3√32
2) (√75 - √12)√3
3) (√7 - 3)²
4) (√5 + 2√2)(√5 - 2√2)

Answer 1

1) 5√2 - 4√8 + 3√32 = 5√2 - 4√(2×4) + 3√(2×16) = 5√2 - 8√2 + 12√2 = 9√2

2) (√75 - √12)√3 = (√(3×25) - √(3×4)) × √3 =

(5√3 - 2√3) × √3 = 3√3 × √3 = 3 × 3 = 9

3) (√7 - 3)² = (√7)² - 2×3×√7 + 3² = 7 - 6√7 + 9 = 16 - 6√7

4) (√5 + 2√2)(√5 - 2√2) = 5 - 2√10 + 2√10 - 8 = -3

Answer 2

$displaystyle tt 1) : 5sqrt{2}-4sqrt{8}+3sqrt{32}=5sqrt{2}-8sqrt{2}+12sqrt{2}=9sqrt{2}\displaystyle tt 2) : (sqrt{75}-sqrt{12})sqrt{3}=(5sqrt{3}-2sqrt{3})sqrt{3}=3sqrt{3}sqrt{3}=3cdot3=9\displaystyle tt 3) : (sqrt{7}-3)^2=7-6sqrt{7}+9=16-6sqrt{7}\displaystyle tt 4) : (sqrt{5}+2sqrt{2})(sqrt{5}-2sqrt{2})=5-4cdot2=5-8=-3$