Question

Помогите с алгеброй, пожалуйста!

Answer 1

$\frac{10}{ \sqrt{5} } = \frac{10* \sqrt{5} }{ \sqrt{5}* \sqrt{5} } = \frac{10 \sqrt{5} }{5} =2 \sqrt{5}\\\\ \frac{a}{ \sqrt[3]{a} }= \frac{ \sqrt[3]{ a^{3} } }{ \sqrt[3]{a} }= \sqrt[3]{ a^{2} } \\\\ \frac{1}{1- \sqrt{3} } = \frac{1*(1+ \sqrt{3}) }{(1- \sqrt{3})(1+ \sqrt{3} ) }= \frac{1+ \sqrt{3} }{1 ^{2}-( \sqrt{3}) ^{2} }= \frac{1+ \sqrt{3} }{1-3}=- \frac{1+ \sqrt{3} }{2} \\\\ \frac{ \sqrt{a+b} }{ \sqrt{a-b} }= \frac{ \sqrt{a+b}* \sqrt{a-b} }{ \sqrt{a-b}* \sqrt{a-b} } =$$\frac{ \sqrt{ a^{2}- b^{2} } }{a-b} \frac{a}{ \sqrt{ \sqrt{a} } } = \frac{a}{ \sqrt[4]{a} } = \frac{ \sqrt[4]{ a^{4} } }{ \sqrt[4]{a} }= \sqrt[4]{ a^{3} }$

Answer 2

$\displaystyle a)..\frac{10}{ \sqrt{5}}= \frac{10* \sqrt{5}}{ \sqrt{5}* \sqrt{5}}= \frac{10 \sqrt{5}}{5}=2 \sqrt{5}; \\ \\ b).. \frac{a}{ \sqrt[3]{a}}= \frac{a* \sqrt[3]{a^{2}} }{ \sqrt[3]{a}* \sqrt[3]{a^{2}}}= \frac{a* \sqrt[3]{a^{2}} }{\sqrt[3]{a^{3}}}= \sqrt[3]{a^{2}}; \\ \\ c).. \frac{1}{1- \sqrt{3}}= \frac{1+ \sqrt{3}}{(1- \sqrt{3})(1+ \sqrt{3)}}}= \frac{1+ \sqrt{3}}{1-3}=- \frac{1+ \sqrt{3}}{2};$
$\displaystyle d).. \frac{ \sqrt{a+b}}{ \sqrt{a-b}}= \frac{\sqrt{a+b}*\sqrt{a-b}}{\sqrt{a-b}*\sqrt{a-b}}= \frac{\sqrt{a^{2}-b^{2}}}{a-b}; \\ \\ \\e).. \frac{a}{\sqrt{\sqrt{a}}}= \frac{a}{a^{1/4}}=a^{1-1/4}=a^{3/4}=\sqrt[4]{a^{3}};$