Question

Помогите пожалуйста :((((((

Answer 1

№4

1) $7\sqrt{6}-2\sqrt{54}+\sqrt{96}=7\sqrt{6}-2\sqrt{9}\sqrt{6}+\sqrt{16}\sqrt{6}=7\sqrt{6}-6\sqrt{6}+4\sqrt{6}=5\sqrt{6}$

2)

$(\sqrt{80}-\sqrt{20})\sqrt{5}=\sqrt{80*5}-\sqrt{20*5}=\sqrt{400}-\sqrt{100}=20-10=10$

3)

$(\sqrt{10}-1)^2=(\sqrt{10})^2-2*\sqrt{10}*1+1^2=10+1-2\sqrt{10}=11-2\sqrt{10}$

4)

$(6\sqrt{3}+\sqrt{2})(6\sqrt{3}-\sqrt{2})=(6\sqrt{3})^2-(\sqrt{2})^2=36*3-2=108-2=106$

№5

1)

$4\sqrt{5}=\sqrt{16}\sqrt{5}=\sqrt{16*5}=\sqrt{80}\\3\sqrt{8}=\sqrt{9}\sqrt{8}=\sqrt{9*5}=\sqrt{72}\\80>72; \sqrt{80}>\sqrt{72}\\4\sqrt{5}>3\sqrt{8}$

2)

$7\sqrt{\frac{2}{7}}=\sqrt{49}\sqrt{\frac{2}{7}}=\sqrt{\frac{49*2}{7}}=\sqrt{14}\\\frac{1}{2}\sqrt{56}=\sqrt{\frac{1}{4}}\sqrt{56}=\sqrt{\frac{56}{4}}=\sqrt{14}\\7\sqrt{\frac{2}{7}}=\frac{1}{2}\sqrt{56}$