Question

упростите √40+√1/40 + √90 + √1/90

Answer 1

$\sqrt{40}+ \sqrt{ \frac{1}{40} } + \sqrt{90} + \sqrt{ \frac{1}{90} } =$

$2 \sqrt{10}+ \sqrt{ \frac{40}{1600} } + 3\sqrt{10} + \sqrt{ \frac{90}{8100} } =$

$5\sqrt{10}+ \frac{ \sqrt{40} }{ \sqrt{1600} }+ \frac{ \sqrt{90} }{ \sqrt{8100} } =$

$5\sqrt{10}+ \frac{2 \sqrt{10} }{40}+ \frac{3 \sqrt{10} }{90} =$

$5\sqrt{10}+ \frac{18 \sqrt{10} }{360}+ \frac{12 \sqrt{10} }{360} =$

$5\sqrt{10}+ \frac{30\sqrt{10} }{360}=$

$5\sqrt{10}+ \frac{\sqrt{10} }{12}=$

$\frac{60\sqrt{10}}{12} + \frac{\sqrt{10} }{12}= \frac{61\sqrt{10} }{12}$

Answer 2

$\sqrt{40}+\sqrt{\frac{1}{40}}+\sqrt{90}+\sqrt{\frac{1}{90}}=\sqrt{40}+\frac{1}{\sqrt{40}}+\sqrt{90}+\frac{1}{\sqrt{90}}=\\\\=\frac{40+1}{\sqrt{40}}+\frac{90+1}{\sqrt{90}} =\frac{41}{2\sqrt{10}}+\frac{91}{3\sqrt{10}}=\frac{3\cdot 41+2\cdot 91}{6\sqrt{10}}=\frac{305}{6\sqrt{10}}=\frac{305\sqrt{10}}{60}=\frac{61\sqrt{10}}{12}$