tolong kakk mau dikumpulin (yang asal di report).... Question from @araachanx48

August 2022 1 2 Report

tolong kakk mau dikumpulin (yang asal di report)

JΟY

Bentuk sederhana dari:

$\begin{aligned}&{\sf{1.~\frac{\sqrt{\sf2}}{6\sqrt{\sf3}}={\boldsymbol{\frac{\sqrt{\textsf{\textbf{6}}}}{\textsf{\textbf{18}}}}}}}\\&{\sf{2.~\frac{2\sqrt{\sf5}}{3+\sqrt{\sf5}}={\boldsymbol{\frac{\textsf{\textbf{3}}\sqrt{\textsf{\textbf{5}}}-\textsf{\textbf{5}}}{\textsf{\textbf{2}}}}}}}\\&{\sf{3.~\frac{2\sqrt{\sf{10}}}{\sqrt{\sf7}-\sqrt{ \sf5}}={\boldsymbol{\sqrt{\textsf{\textbf{70}}}+\textsf{\textbf{5}}\sqrt{\textsf{\textbf{2}}}}}}}\end{aligned}$

Pembahasan

–› No. 1

$\begin{aligned}{\sf{\frac{\sqrt{\sf2}}{6\sqrt{\sf3}}}}&={\sf{\frac{\sqrt{\sf2}}{6\sqrt{\sf3}}\times\frac{6\sqrt{\sf3}}{6\sqrt{\sf3}}}}\\&={\sf{\frac{\sqrt{\sf2}\left(6\sqrt{\sf3}\right)}{\left(6\sqrt{\sf3}\right)\left(6\sqrt{\sf3}\right)}}}\\&={\sf{\frac{\sqrt{\sf2}\left(6\sqrt{\sf3}\right)}{\left(36\right)\left(3\right)}}}\\&={\sf{\frac{6\sqrt{\sf6}}{108}}}\\&={\sf{\frac{\sqrt{\sf6}}{18}}}\end{aligned}$

–› No. 2

$\begin{aligned}{\sf{\frac{2\sqrt{\sf5}}{3+\sqrt{\sf5}}}}&={\sf{\frac{2\sqrt{\sf5}}{3+\sqrt{\sf5}}\times\frac{3-\sqrt{\sf5}}{3-\sqrt{\sf5}}}}\\&={\sf{\frac{2\sqrt{\sf5}\left(3-\sqrt{\sf5}\right)}{\left(3+\sqrt{\sf5}\right)\left(3-\sqrt{\sf5}\right)}}}\\&={\sf{\frac{2\sqrt{\sf5}\left(3-\sqrt{\sf5}\right)}{9-5}}}\\&={\sf{\frac{6\sqrt{\sf5}-10}{4}}}\\&={\sf{\frac{3\sqrt{\sf5}-5}{2}}}\end{aligned}$

–› No. 3

$\begin{aligned}{\sf{\frac{2\sqrt{\sf{10}}}{\sqrt{\sf7}-\sqrt{ \sf5}}}}&={\sf{\frac{2\sqrt{\sf{10}}}{\sqrt{\sf7}-\sqrt{\sf5}}\times\frac{\sqrt{\sf7}+\sqrt{\sf5}}{\sqrt{\sf7}+\sqrt{\sf5}}}}\\&={\sf{\frac{2\sqrt{\sf{10}}\left(\sqrt{\sf7}+\sqrt{\sf5}\right)}{\left(\sqrt{\sf7}-\sqrt{\sf5}\right)\left(\sqrt{\sf7}+\sqrt{\sf5}\right)}}}\\&={\sf{\frac{2\sqrt{\sf{10}}\left(\sqrt{\sf7}+\sqrt{\sf5}\right)}{7-5}}}\\&={\sf{\frac{2\sqrt{\sf{70}}+10\sqrt{\sf2}}{2}}}\\&={\sf{\sqrt{\sf{70}}+5\sqrt{\sf2}}}\end{aligned}$