3000000-3000000-4000000-4000000-

Question Number 139278 by Agnibhoo last updated on 25/Apr/21

\sqrt{\frac{3000000 + 3000000}{4000000 + 4000000}} = ?

Answered by Rasheed.Sindhi last updated on 25/Apr/21

\sqrt{\frac{6 \times 1000000}{8 \times 1000000}} = \frac{\sqrt{3}}{2}

Commented by otchereabdullai@gmail.com last updated on 25/Apr/21

nice shortcut

Answered by Opredador last updated on 25/Apr/21

\sqrt{\frac{6000000}{8000000}} \Rightarrow \sqrt{\frac{6 \times 10^{6}}{8 \times 10^{6}}} \Rightarrow \frac{\sqrt{6 \times 10^{6}}}{\sqrt{8 \times 10^{6}}}

\Rightarrow \frac{\sqrt{6} \times \sqrt{10^{6}}}{\sqrt{8} \times \sqrt{10^{6}}} \Rightarrow \frac{\sqrt{6} \times 10^{\frac{6}{2}}}{\sqrt{8} \times 10^{\frac{6}{2}}} \Rightarrow \frac{\sqrt{6} \times 10^{3}}{\sqrt{8} \times 10^{3}}

\Rightarrow \frac{10^{3}}{10^{3}} \times \frac{\sqrt{6}}{\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}} \Rightarrow \frac{\sqrt{6} \times \sqrt{8}}{\sqrt{8 \times 8}} \Rightarrow \frac{\sqrt{6} \times \sqrt{2^{3}}}{\sqrt{8^{2}}}

\Rightarrow \frac{\sqrt{6} \times \sqrt{2^{2} \times 2}}{8} \Rightarrow \frac{\sqrt{6} \times \sqrt{2^{2}} \times \sqrt{2}}{8} \Rightarrow \frac{\sqrt{6} \times 2 \times \sqrt{2}}{2 \times 4}

\Rightarrow \frac{\sqrt{6} \times 2 \times \sqrt{2}}{2 \times 4} \Rightarrow \frac{\sqrt{6} \times \sqrt{2}}{4} \Rightarrow \frac{\sqrt{2 \times 6}}{4}

\Rightarrow \frac{\sqrt{2 \times 2 \times 3}}{4} \Rightarrow \frac{\sqrt{2^{2} \times 3}}{4} \Rightarrow \frac{\sqrt{2^{2}} \times \sqrt{3}}{4}

\Rightarrow \frac{2 \times \sqrt{3}}{4} \Rightarrow \frac{2 \sqrt{3}}{2 \times 2} = \frac{\sqrt{3}}{2}

\frac{\sqrt{3}}{2} \approx 0.866025

\sqrt{\frac{3000000 + 3000000}{4000000 + 4000000}} \approx 0.866025