Question

How to prove that (2/5)(sqrt(H/2g)) is equal to
(1/5)(sqrt(2H/g)) ?

Answer 1

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

Answer 2

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)

Answer 3

Thanks :) That was really helpful :)

Answer 4

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