Simplify i square root of 6*i square root of 1/3

$i \sqrt{6} \cdot i \sqrt{\frac{1}{3}}$

Rewrite $\sqrt{\frac{1}{3}}$ as $\frac{\sqrt{1}}{\sqrt{3}}$ .

$i \sqrt{6} \cdot (i \frac{\sqrt{1}}{\sqrt{3}})$

Any root of $1$ is $1$ .

$i \sqrt{6} \cdot (i \frac{1}{\sqrt{3}})$

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$i \sqrt{6} \cdot (i (\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}))$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}})$

Raise $\sqrt{3}$ to the power of $1$ .

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}})$

Raise $\sqrt{3}$ to the power of $1$ .

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}})$

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

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}})$

Add $1$ and $1$ .

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{{\sqrt{3}}^{2}})$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}})$

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

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}})$

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

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{3^{\frac{2}{2}}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{3^{\frac{2}{2}}})$

Rewrite the expression.

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{3^{1}})$

Evaluate the exponent.

$i \sqrt{6} \cdot (i \frac{\sqrt{3}}{3})$

Combine $i$ and $\frac{\sqrt{3}}{3}$ .

$i \sqrt{6} \cdot \frac{i \sqrt{3}}{3}$

Multiply $i \sqrt{6} \frac{i \sqrt{3}}{3}$ .

Combine $\frac{i \sqrt{3}}{3}$ and $i$ .

$\frac{i \sqrt{3} i}{3} \sqrt{6}$

Raise $i$ to the power of $1$ .

$\frac{i^{1} i \sqrt{3}}{3} \sqrt{6}$

Raise $i$ to the power of $1$ .

$\frac{i^{1} i^{1} \sqrt{3}}{3} \sqrt{6}$

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

$\frac{i^{1 + 1} \sqrt{3}}{3} \sqrt{6}$

Add $1$ and $1$ .

$\frac{i^{2} \sqrt{3}}{3} \sqrt{6}$

Combine $\frac{i^{2} \sqrt{3}}{3}$ and $\sqrt{6}$ .

$\frac{i^{2} \sqrt{3} \sqrt{6}}{3}$

Combine using the product rule for radicals.

$\frac{i^{2} \sqrt{6 \cdot 3}}{3}$

Multiply $6$ by $3$ .

$\frac{i^{2} \sqrt{18}}{3}$

Simplify the numerator.

Rewrite $i^{2}$ as $- 1$ .

$\frac{- \sqrt{18}}{3}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{- \sqrt{9 (2)}}{3}$

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical.

$\frac{- 1 \cdot 3 \sqrt{2}}{3}$

Multiply $- 1$ by $3$ .

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

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 3 \sqrt{2}$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (- \sqrt{2})}{3 (1)}$

Cancel the common factor.

$\frac{3 (- \sqrt{2})}{3 \cdot 1}$

Rewrite the expression.

$\frac{- \sqrt{2}}{1}$

Divide $- \sqrt{2}$ by $1$ .

$- \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$

Simplify i square root of 6*i square root of 1/3

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