Basic Math Examples

$\sqrt{14} \sqrt{3} \sqrt{7} - \sqrt{54 a^{2}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{14 \cdot 3} \sqrt{7} - \sqrt{54 a^{2}}$

Step 2

Combine using the product rule for radicals.

$\sqrt{14 \cdot 3 \cdot 7} - \sqrt{54 a^{2}}$

Step 3

Multiply $14$ by $3$ .

$\sqrt{42 \cdot 7} - \sqrt{54 a^{2}}$

Step 4

Multiply $42$ by $7$ .

$\sqrt{294} - \sqrt{54 a^{2}}$

Step 5

Rewrite $294$ as $7^{2} \cdot 6$ .

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Step 5.1

Factor $49$ out of $294$ .

$\sqrt{49 (6)} - \sqrt{54 a^{2}}$

Step 5.2

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

$\sqrt{7^{2} \cdot 6} - \sqrt{54 a^{2}}$

$\sqrt{7^{2} \cdot 6} - \sqrt{54 a^{2}}$

Step 6

Pull terms out from under the radical.

$7 \sqrt{6} - \sqrt{54 a^{2}}$

Step 7

Rewrite $54 a^{2}$ as ${(3 a)}^{2} \cdot 6$ .

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Step 7.1

Factor $9$ out of $54$ .

$7 \sqrt{6} - \sqrt{9 (6) a^{2}}$

Step 7.2

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

$7 \sqrt{6} - \sqrt{3^{2} \cdot 6 a^{2}}$

Step 7.3

Move $6$ .

$7 \sqrt{6} - \sqrt{3^{2} a^{2} \cdot 6}$

Step 7.4

Rewrite $3^{2} a^{2}$ as ${(3 a)}^{2}$ .

$7 \sqrt{6} - \sqrt{{(3 a)}^{2} \cdot 6}$

$7 \sqrt{6} - \sqrt{{(3 a)}^{2} \cdot 6}$

Step 8

Pull terms out from under the radical.

$7 \sqrt{6} - (3 a \sqrt{6})$

Step 9

Multiply $3$ by $- 1$ .

$7 \sqrt{6} - 3 a \sqrt{6}$

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