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

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