Question

4÷7 √147 + 3÷8 √192 -1÷5 √75

Answer 1

Answer:

$\frac{4}{7}\sqrt{1}\cdot \:47+\frac{3}{8}\sqrt{1}\cdot \:92-\frac{1}{5}\sqrt{7}\cdot \:5=-\sqrt{7}+\frac{859}{14}\quad \left(\mathrm{Decimal:\quad }\:58.71139\dots \right)$

Step-by-step explanation:

$\frac{4}{7}\sqrt{1}\cdot \:47+\frac{3}{8}\sqrt{1}\cdot \:92-\frac{1}{5}\sqrt{7}\cdot \:5$

$\mathrm{Apply\:rule}\:\sqrt{1}=1$

$=1\cdot \:47\cdot \frac{4}{7}+1\cdot \:92\cdot \frac{3}{8}-5\sqrt{7}\frac{1}{5}$

$=\frac{188}{7}+\frac{69}{2}-\sqrt{7}$

$=\frac{376}{14}+\frac{483}{14}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}$

$=\frac{376+483}{14}$

$\mathrm{Add\:the\:numbers:}\:376+483=859$

$=-\sqrt{7}+\frac{859}{14}$