## anonymous 3 years ago How to prove that (2/5)(sqrt(H/2g)) is equal to (1/5)(sqrt(2H/g)) ?

1. anonymous

$prove that \frac{ 2 }{ 5 } \sqrt{\frac{ H }{ 2g }} is equal \to \frac{ 1 }{ 5 }\sqrt{\frac{ 2H }{ g }}$

2/5 sqrt(H/2g) = 2/5 sqrt(H)/(sqrt(2) * sqrt(g)) multiply by sqrt(2)/sqrt(2) = 2/5 sqrt(H)/(sqrt(2) * sqrt(g)) * sqrt(2)/sqrt(2) = 2/5 sqrt(2H)/((2)*sqrt(g)) = 2/10 * sqrt(2H)/sqrt(g) = 1/5 * sqtr(2H/g)

3. anonymous

Thanks :) That was really helpful :)

4. anonymous

$25\times \left( \frac{ 2 }{ 5 } \times \sqrt{\frac{ H }{ 2g }} \right) = 25\times \left( \frac{ 1 }{ 5 } \times \sqrt{\frac{ 2H }{ g }} \right)$ $10\times \sqrt{\frac{ H }{ 2g }}=5\times \sqrt{\frac{ 2H }{ g }}$ $\left( 10\times \sqrt{\frac{ H }{ 2g }} \right)^{2} = \left( 5\times \sqrt{\frac{ 2H }{ g }} \right)^{2}$ $\frac{ 100H }{ 2g } = \frac{ 25\times2H}{ g }$ $\frac{ 50H }{ g } = \frac{ 50H }{ g }$ $\frac{ H }{ g } = \frac{ H }{ g }$