1) Вычислить: 1) 0,2√4900; 2) 100√0,04 − ¹⁄₁₇√289; 3) ⁷⁄₈ − √(15/49); 4) √361 − 10√289; 5) 3,6·√0,25 + ¹⁄₃₂·√256; 6) 8·√(5 ¹⁄₁₆) + 3.

Question

Вопрос:

Accepted Answer

\(0{,}2\sqrt{4900}=0{,}2\cdot70=14\).
\(100\sqrt{0{,}04}-\frac{1}{17}\sqrt{289=100\cdot0{,}2-\frac{1}{17}\cdot17=20-1=19\).
\(\frac{7}{8}-\sqrt{\frac{15}{49}}=\frac{7}{8}-\frac{\sqrt{15}}{7}=\frac{49-8\sqrt{15}}{56}\).
\(\sqrt{361}-10\sqrt{289}=19-10\cdot17=19-170=-151\).
\(3{,}6\cdot\sqrt{0{,}25}+\frac{1}{32}\cdot\sqrt{256}=3{,}6\cdot0{,}5+\frac{1}{32}\cdot16=1{,}8+0{,}5=2{,}3\).
\(8\cdot\sqrt{5\frac{1}{16}}+3=8\cdot\sqrt{\frac{81}{16}}+3=8\cdot\frac{9}{4}+3=21\).

Ответ: 1) 14; 2) 19; 3) \(\frac{49-8\sqrt{15}}{56}\); 4) −151; 5) 2,3; 6) 21.