Solve for a (5 square root of a)/4=20

$\frac{5 \sqrt{a}}{4} = 20$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 \sqrt{a}}{4} = \frac{4}{5} \cdot 20$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{5} \cdot \frac{5 \sqrt{a}}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 \sqrt{a}}{4} = \frac{4}{5} \cdot 20$

Rewrite the expression.

$\frac{1}{5} (5 \sqrt{a}) = \frac{4}{5} \cdot 20$

Cancel the common factor of $5$ .

Factor $5$ out of $5 \sqrt{a}$ .

$\frac{1}{5} (5 (\sqrt{a})) = \frac{4}{5} \cdot 20$

Cancel the common factor.

$\frac{1}{5} (5 \sqrt{a}) = \frac{4}{5} \cdot 20$

Rewrite the expression.

$\sqrt{a} = \frac{4}{5} \cdot 20$

Simplify the right side.

Simplify $\frac{4}{5} \cdot 20$ .

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\sqrt{a} = \frac{4}{5} \cdot (5 (4))$

Cancel the common factor.

$\sqrt{a} = \frac{4}{5} \cdot (5 \cdot 4)$

Rewrite the expression.

$\sqrt{a} = 4 \cdot 4$

Multiply $4$ by $4$ .

$\sqrt{a} = 16$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{a}}^{2} = 16^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$ .

${(a^{\frac{1}{2}})}^{2} = 16^{2}$

Simplify the left side.

Simplify ${(a^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${(a^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a^{\frac{1}{2} \cdot 2} = 16^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a^{\frac{1}{2} \cdot 2} = 16^{2}$

Rewrite the expression.

$a^{1} = 16^{2}$

Simplify.

$a = 16^{2}$

Simplify the right side.

Raise $16$ to the power of $2$ .

$a = 256$

Solve for a (5 square root of a)/4=20

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