Basic Math Examples

6 \div \sqrt{70}

$6 \div \sqrt{70}$

Step 1

Rewrite the division as a fraction.

\frac{6}{\sqrt{70}}

$\frac{6}{\sqrt{70}}$

Step 2

Multiply

\frac{6}{\sqrt{70}}

$\frac{6}{\sqrt{70}}$ by

\frac{\sqrt{70}}{\sqrt{70}}

$\frac{\sqrt{70}}{\sqrt{70}}$ .

\frac{6}{\sqrt{70}} \cdot \frac{\sqrt{70}}{\sqrt{70}}

$\frac{6}{\sqrt{70}} \cdot \frac{\sqrt{70}}{\sqrt{70}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply

\frac{6}{\sqrt{70}}

$\frac{6}{\sqrt{70}}$ by

\frac{\sqrt{70}}{\sqrt{70}}

$\frac{\sqrt{70}}{\sqrt{70}}$ .

\frac{6 \sqrt{70}}{\sqrt{70} \sqrt{70}}

$\frac{6 \sqrt{70}}{\sqrt{70} \sqrt{70}}$

Step 3.2

Raise

\sqrt{70}

$\sqrt{70}$ to the power of

1

$1$ .

\frac{6 \sqrt{70}}{{\sqrt{70}}^{1} \sqrt{70}}

$\frac{6 \sqrt{70}}{{\sqrt{70}}^{1} \sqrt{70}}$

Step 3.3

Raise

\sqrt{70}

$\sqrt{70}$ to the power of

1

$1$ .

\frac{6 \sqrt{70}}{{\sqrt{70}}^{1} {\sqrt{70}}^{1}}

$\frac{6 \sqrt{70}}{{\sqrt{70}}^{1} {\sqrt{70}}^{1}}$

Step 3.4

Use the power rule

a^{m} a^{n} = a^{m + n}

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

\frac{6 \sqrt{70}}{{\sqrt{70}}^{1 + 1}}

$\frac{6 \sqrt{70}}{{\sqrt{70}}^{1 + 1}}$

Step 3.5

Add

1

$1$ and

1

$1$ .

\frac{6 \sqrt{70}}{{\sqrt{70}}^{2}}

$\frac{6 \sqrt{70}}{{\sqrt{70}}^{2}}$

Step 3.6

Rewrite

{\sqrt{70}}^{2}

${\sqrt{70}}^{2}$ as

70

$70$ .

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Step 3.6.1

Use

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

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

\sqrt{70}

$\sqrt{70}$ as

70^{\frac{1}{2}}

$70^{\frac{1}{2}}$ .

\frac{6 \sqrt{70}}{{(70^{\frac{1}{2}})}^{2}}

$\frac{6 \sqrt{70}}{{(70^{\frac{1}{2}})}^{2}}$

Step 3.6.2

Apply the power rule and multiply exponents,

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

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

\frac{6 \sqrt{70}}{70^{\frac{1}{2} \cdot 2}}

$\frac{6 \sqrt{70}}{70^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\frac{6 \sqrt{70}}{70^{\frac{2}{2}}}

$\frac{6 \sqrt{70}}{70^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of

2

$2$ .

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Step 3.6.4.1

Cancel the common factor.

\frac{6 \sqrt{70}}{70^{\frac{2}{2}}}

$\frac{6 \sqrt{70}}{70^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

\frac{6 \sqrt{70}}{70^{1}}

$\frac{6 \sqrt{70}}{70^{1}}$

\frac{6 \sqrt{70}}{70^{1}}

$\frac{6 \sqrt{70}}{70^{1}}$

Step 3.6.5

Evaluate the exponent.

\frac{6 \sqrt{70}}{70}

$\frac{6 \sqrt{70}}{70}$

\frac{6 \sqrt{70}}{70}

$\frac{6 \sqrt{70}}{70}$

\frac{6 \sqrt{70}}{70}

$\frac{6 \sqrt{70}}{70}$

Step 4

Cancel the common factor of

6

$6$ and

70

$70$ .

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Step 4.1

Factor

2

$2$ out of

6 \sqrt{70}

$6 \sqrt{70}$ .

\frac{2 (3 \sqrt{70})}{70}

$\frac{2 (3 \sqrt{70})}{70}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

2

$2$ out of

70

$70$ .

\frac{2 (3 \sqrt{70})}{2 (35)}

$\frac{2 (3 \sqrt{70})}{2 (35)}$

Step 4.2.2

Cancel the common factor.

\frac{2 (3 \sqrt{70})}{2 \cdot 35}

$\frac{2 (3 \sqrt{70})}{2 \cdot 35}$

Step 4.2.3

Rewrite the expression.

\frac{3 \sqrt{70}}{35}

$\frac{3 \sqrt{70}}{35}$

\frac{3 \sqrt{70}}{35}

$\frac{3 \sqrt{70}}{35}$

\frac{3 \sqrt{70}}{35}

$\frac{3 \sqrt{70}}{35}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{3 \sqrt{70}}{35}

$\frac{3 \sqrt{70}}{35}$

Decimal Form:

0.71713716 \dots

$0.71713716 \dots$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$