Question

$(2 \sqrt{5} \div 4)^{2}$
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Answer 1

$\large\textsf\red{QUESTION:}$

$(2 \sqrt{5} \div 4)^{2}$

$\large\textsf\green{ANSWER:}$

$\green{\sf{} \dfrac{5}{4}}$

$\textsf\blue{\underline{SOLUTION:}}$

$\textsf{Step\:1:}$ Write the division as a fraction

$\implies{\sf{} \dfrac{(2 \sqrt{5}{4})²}}$

$\textsf{Step\:2:}$ Cancel the fraction with 2

$\implies{\sf{} \dfrac{(\cancel{2}} \sqrt{5}}{\cancel{4}})²}}$

$\implies{\sf{} \dfrac{(\sqrt{5} {2})²}}$

$\textsf\red{\underline{Note:}}$ To raise a fraction to a power, raise the numerator and the denominator to that power.

$\implies{\sf{} \dfrac{\sqrt{5²}}{2²}}$

$\textsf{Step\:3:}$ Reduce the index of the radical and exponent with 2

$\implies{\sf{} \dfrac{5}{2²}}$

$\textsf{Lastly:}$ Evaluate the power

$\green\implies\green{\sf{} \dfrac{5}{4}}$

hope this help!

Answer 2

Question:-

($\dfrac{2√5}{4}$) ²

$\dfrac{4×5}{16}$ = $\dfrac{5}{4}$