Rationalize the Numerator square root of 2/3

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

Split the fraction inside the radical into a separate radical expression in the numerator and the denominator. A fraction of roots is equivalent to a root of the fraction.

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

Remove the parentheses around the expression $\frac{\sqrt{2}}{\sqrt{3}}$ .

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

Rationalize the numerator.

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

Simplify.

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

Combine using the product rule for radicals.

$\frac{\sqrt{2 \cdot 2}}{\sqrt{3} (\sqrt{2})}$

Write the expression using exponents.

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Multiply $2$ by $2$ .

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

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

$\frac{\sqrt{2^{2}}}{\sqrt{3} (\sqrt{2})}$

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

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$\frac{2}{\sqrt{6}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{\sqrt{6}}$

Decimal Form:

$0.81649658 \dots$

Rationalize the Numerator square root of 2/3

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