Linear Algebra Examples

$\frac{2 i \sqrt{5}}{i \sqrt{2}}$

Step 1

Cancel the common factor of

$i$ .

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Step 1.1

Cancel the common factor.

$\frac{2 i \sqrt{5}}{i \sqrt{2}}$

Step 1.2

Rewrite the expression.

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

Step 2

Multiply

$\frac{2 \sqrt{5}}{\sqrt{2}}$ by

$\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply

$\frac{2 \sqrt{5}}{\sqrt{2}}$ by

$\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 3.2

Raise

$\sqrt{2}$ to the power of

$1$ .

$\frac{2 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Step 3.3

Raise

$\sqrt{2}$ to the power of

$1$ .

$\frac{2 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Step 3.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.5

Add

$1$ and

$1$ .

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

Step 3.6

Rewrite

${\sqrt{2}}^{2}$ as

$2$ .

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Step 3.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{2}$ as

$2^{\frac{1}{2}}$ .

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

Step 3.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 3.6.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 3.6.4

Cancel the common factor of

$2$ .

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Step 3.6.4.1

Cancel the common factor.

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

Step 3.6.4.2

Rewrite the expression.

$\frac{2 \sqrt{5} \sqrt{2}}{2^{1}}$

Step 3.6.5

Evaluate the exponent.

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

Step 4

Cancel the common factor of

$2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide

$\sqrt{5} \sqrt{2}$ by

$1$ .

$\sqrt{5} \sqrt{2}$

Step 5

Combine using the product rule for radicals.

$\sqrt{5 \cdot 2}$

Step 6

Multiply

$5$ by

$2$ .

$\sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$