Simplify square root of 2/5* square root of 2/3

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

Step 1

Combine using the product rule for radicals.

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

Step 2

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

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

Step 3

Multiply.

Multiply $2$ by $2$ .

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

Multiply $5$ by $3$ .

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

Step 4

Rewrite $\sqrt{\frac{4}{15}}$ as $\frac{\sqrt{4}}{\sqrt{15}}$ .

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

Step 5

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2^{2}}}{\sqrt{15}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2}{\sqrt{15}}$

Step 6

Multiply $\frac{2}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{2}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}}$

Step 7

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{2 \sqrt{15}}{\sqrt{15} \sqrt{15}}$

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{2 \sqrt{15}}{{\sqrt{15}}^{1} \sqrt{15}}$

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{2 \sqrt{15}}{{\sqrt{15}}^{1} {\sqrt{15}}^{1}}$

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

$\frac{2 \sqrt{15}}{{\sqrt{15}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{15}}{{\sqrt{15}}^{2}}$

Rewrite ${\sqrt{15}}^{2}$ as $15$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15}$ as $15^{\frac{1}{2}}$ .

$\frac{2 \sqrt{15}}{{(15^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{15}}{15^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{15}}{15^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{15}}{15^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{15}}{15^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{15}}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{15}}{15}$

Decimal Form:

$0.51639777 \dots$

Simplify square root of 2/5* square root of 2/3

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