deksteenk9

2022-10-08

How should this fraction involving powers be solved

$\sqrt{5}\cdot {\left(\frac{5}{4}\right)}^{\frac{1}{2}}$

All I know is that this can be written as

$\sqrt{5}\cdot {\left(\frac{5}{{2}^{2}}\right)}^{\frac{1}{2}}$

Any Ideas?

$\sqrt{5}\cdot {\left(\frac{5}{4}\right)}^{\frac{1}{2}}$

All I know is that this can be written as

$\sqrt{5}\cdot {\left(\frac{5}{{2}^{2}}\right)}^{\frac{1}{2}}$

Any Ideas?

smh3402en

Beginner2022-10-09Added 11 answers

$\sqrt{5}{\left(\frac{5}{4}\right)}^{\frac{1}{2}}={5}^{\frac{1}{2}}\cdot {\left(\frac{5}{{2}^{2}}\right)}^{\frac{1}{2}}={5}^{\frac{1}{2}}\cdot \frac{{5}^{\frac{1}{2}}}{{\left({2}^{2}\right)}^{\frac{1}{2}}}=\frac{{5}^{\frac{1}{2}+\frac{1}{2}}}{2}=\frac{5}{2}$

Leonel Schwartz

Beginner2022-10-10Added 2 answers

$\sqrt{5}\left(\frac{\sqrt{5}}{\sqrt{4}}\right)=$$\left(\frac{\sqrt{5\ast 5}}{2}\right)$=$\left(\frac{\sqrt{25}}{2}\right)$=$\frac{5}{2}$

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