Evaluate (4 square root of 2)/(3 square root of 5)

$\frac{4 \sqrt{2}}{3 \sqrt{5}}$

Step 1

Multiply $\frac{4 \sqrt{2}}{3 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{4 \sqrt{2}}{3 \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{4 \sqrt{2}}{3 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 \sqrt{5} \sqrt{5}}$

Move $\sqrt{5}$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 (\sqrt{5} \sqrt{5})}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 ({\sqrt{5}}^{1} \sqrt{5})}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 \sqrt{2} \sqrt{5}}{3 {\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 {\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 {(5^{\frac{1}{2}})}^{2}}$

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

$\frac{4 \sqrt{2} \sqrt{5}}{3 \cdot 5^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{4 \sqrt{2} \sqrt{5}}{3 \cdot 5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{2} \sqrt{5}}{3 \cdot 5^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{4 \sqrt{2} \sqrt{5}}{3 \cdot 5^{1}}$

Evaluate the exponent.

$\frac{4 \sqrt{2} \sqrt{5}}{3 \cdot 5}$

Step 3

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{4 \sqrt{5 \cdot 2}}{3 \cdot 5}$

Multiply $5$ by $2$ .

$\frac{4 \sqrt{10}}{3 \cdot 5}$

Step 4

Multiply $3$ by $5$ .

$\frac{4 \sqrt{10}}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{10}}{15}$

Decimal Form:

$0.84327404 \dots$

Evaluate (4 square root of 2)/(3 square root of 5)

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