Solve {left(sqrt{5}*sqrt[4]{25}right)}^2

$${ \left( \sqrt{ 5 } \times \sqrt[ 4 ]{ 25 } \right) }^{ 2 }$$

Evaluate

$$25$$

Solution Steps

Rewrite \sqrt[4]{25} as \sqrt[4]{5^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{25}=\sqrt[4]{5^{2}}=5^{\frac{2}{4}}=5^{\frac{1}{2}}=\sqrt{5}$$

Insert the obtained value back in the expression.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25$$

Factor

$$5^{2}$$