Linear Algebra Examples

$\frac{69465}{\sqrt{56565}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $56565$ as $3^{2} \cdot 6285$ .

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Step 1.1.1

Factor $9$ out of $56565$ .

$\frac{69465}{\sqrt{9 (6285)}}$

Step 1.1.2

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

$\frac{69465}{\sqrt{3^{2} \cdot 6285}}$

Step 1.2

Pull terms out from under the radical.

$\frac{69465}{3 \sqrt{6285}}$

Step 2

Cancel the common factor of $69465$ and $3$ .

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Step 2.1

Factor $3$ out of $69465$ .

$\frac{3 \cdot 23155}{3 \sqrt{6285}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $3 \sqrt{6285}$ .

$\frac{3 \cdot 23155}{3 (\sqrt{6285})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 \cdot 23155}{3 \sqrt{6285}}$

Step 2.2.3

Rewrite the expression.

$\frac{23155}{\sqrt{6285}}$

Step 3

Multiply $\frac{23155}{\sqrt{6285}}$ by $\frac{\sqrt{6285}}{\sqrt{6285}}$ .

$\frac{23155}{\sqrt{6285}} \cdot \frac{\sqrt{6285}}{\sqrt{6285}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{23155}{\sqrt{6285}}$ by $\frac{\sqrt{6285}}{\sqrt{6285}}$ .

$\frac{23155 \sqrt{6285}}{\sqrt{6285} \sqrt{6285}}$

Step 4.2

Raise $\sqrt{6285}$ to the power of $1$ .

$\frac{23155 \sqrt{6285}}{{\sqrt{6285}}^{1} \sqrt{6285}}$

Step 4.3

Raise $\sqrt{6285}$ to the power of $1$ .

$\frac{23155 \sqrt{6285}}{{\sqrt{6285}}^{1} {\sqrt{6285}}^{1}}$

Step 4.4

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

$\frac{23155 \sqrt{6285}}{{\sqrt{6285}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{23155 \sqrt{6285}}{{\sqrt{6285}}^{2}}$

Step 4.6

Rewrite ${\sqrt{6285}}^{2}$ as $6285$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6285}$ as $6285^{\frac{1}{2}}$ .

$\frac{23155 \sqrt{6285}}{{(6285^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{23155 \sqrt{6285}}{6285^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{23155 \sqrt{6285}}{6285^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{23155 \sqrt{6285}}{6285^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{23155 \sqrt{6285}}{6285^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{23155 \sqrt{6285}}{6285}$

Step 5

Cancel the common factor of $23155$ and $6285$ .

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Step 5.1

Factor $5$ out of $23155 \sqrt{6285}$ .

$\frac{5 (4631 \sqrt{6285})}{6285}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $6285$ .

$\frac{5 (4631 \sqrt{6285})}{5 (1257)}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (4631 \sqrt{6285})}{5 \cdot 1257}$

Step 5.2.3

Rewrite the expression.

$\frac{4631 \sqrt{6285}}{1257}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4631 \sqrt{6285}}{1257}$

Decimal Form:

$292.07349283 \dots$