Basic Math Examples

$A = \sqrt{8} (3 \sqrt{18})$

Step 1

Remove parentheses.

$A = \sqrt{8} \cdot (3 \sqrt{18})$

Step 2

Simplify $\sqrt{8} \cdot (3 \sqrt{18})$ .

Tap for more steps...

Step 2.1

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 2.1.1

Factor $4$ out of $8$ .

$A = \sqrt{4 (2)} \cdot (3 \sqrt{18})$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$A = \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{18})$

Step 2.2

Pull terms out from under the radical.

$A = 2 \sqrt{2} \cdot (3 \sqrt{18})$

Step 2.3

Rewrite $18$ as $3^{2} \cdot 2$ .

Tap for more steps...

Step 2.3.1

Factor $9$ out of $18$ .

$A = 2 \sqrt{2} \cdot (3 \sqrt{9 (2)})$

Step 2.3.2

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

$A = 2 \sqrt{2} \cdot (3 \sqrt{3^{2} \cdot 2})$

Step 2.4

Pull terms out from under the radical.

$A = 2 \sqrt{2} \cdot (3 (3 \sqrt{2}))$

Step 2.5

Multiply $3$ by $3$ .

$A = 2 \sqrt{2} \cdot (9 \sqrt{2})$

Step 2.6

Multiply $2 \sqrt{2} (9 \sqrt{2})$ .

Tap for more steps...

Step 2.6.1

Multiply $9$ by $2$ .

$A = 18 \sqrt{2} \sqrt{2}$

Step 2.6.2

Raise $\sqrt{2}$ to the power of $1$ .

$A = 18 ({\sqrt{2}}^{1} \sqrt{2})$

Step 2.6.3

Raise $\sqrt{2}$ to the power of $1$ .

$A = 18 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 2.6.4

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

$A = 18 {\sqrt{2}}^{1 + 1}$

Step 2.6.5

Add $1$ and $1$ .

$A = 18 {\sqrt{2}}^{2}$

Step 2.7

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

Tap for more steps...

Step 2.7.1

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

$A = 18 {(2^{\frac{1}{2}})}^{2}$

Step 2.7.2

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

$A = 18 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 2.7.3

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

$A = 18 \cdot 2^{\frac{2}{2}}$

Step 2.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.7.4.1

Cancel the common factor.

$A = 18 \cdot 2^{\frac{2}{2}}$

Step 2.7.4.2

Rewrite the expression.

$A = 18 \cdot 2^{1}$

Step 2.7.5

Evaluate the exponent.

$A = 18 \cdot 2$

Step 2.8

Multiply $18$ by $2$ .

$A = 36$