Basic Math Examples

$\sqrt{49 c^{3}} + \sqrt{81 c^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $49 c^{3}$ as ${(7 c)}^{2} c$ .

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Step 1.1.1

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} c^{3}} + \sqrt{81 c^{3}}$

Step 1.1.2

Factor out $c^{2}$ .

$\sqrt{7^{2} (c^{2} c)} + \sqrt{81 c^{3}}$

Step 1.1.3

Rewrite $7^{2} c^{2}$ as ${(7 c)}^{2}$ .

$\sqrt{{(7 c)}^{2} c} + \sqrt{81 c^{3}}$

$\sqrt{{(7 c)}^{2} c} + \sqrt{81 c^{3}}$

Step 1.2

Pull terms out from under the radical.

$7 c \sqrt{c} + \sqrt{81 c^{3}}$

Step 1.3

Rewrite $81 c^{3}$ as ${(9 c)}^{2} c$ .

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Step 1.3.1

Rewrite $81$ as $9^{2}$ .

$7 c \sqrt{c} + \sqrt{9^{2} c^{3}}$

Step 1.3.2

Factor out $c^{2}$ .

$7 c \sqrt{c} + \sqrt{9^{2} (c^{2} c)}$

Step 1.3.3

Rewrite $9^{2} c^{2}$ as ${(9 c)}^{2}$ .

$7 c \sqrt{c} + \sqrt{{(9 c)}^{2} c}$

$7 c \sqrt{c} + \sqrt{{(9 c)}^{2} c}$

Step 1.4

Pull terms out from under the radical.

$7 c \sqrt{c} + 9 c \sqrt{c}$

$7 c \sqrt{c} + 9 c \sqrt{c}$

Step 2

Add $7 c \sqrt{c}$ and $9 c \sqrt{c}$ .

$16 c \sqrt{c}$

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