Basic Math Examples

$(3 - \sqrt{2}) (3 + \sqrt{8})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Factor $4$ out of $8$ .

$(3 - \sqrt{2}) (3 + \sqrt{4 (2)})$

Step 1.1.2

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

$(3 - \sqrt{2}) (3 + \sqrt{2^{2} \cdot 2})$

Step 1.2

Pull terms out from under the radical.

$(3 - \sqrt{2}) (3 + 2 \sqrt{2})$

Step 2

Expand $(3 - \sqrt{2}) (3 + 2 \sqrt{2})$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$3 (3 + 2 \sqrt{2}) - \sqrt{2} (3 + 2 \sqrt{2})$

Step 2.2

Apply the distributive property.

$3 \cdot 3 + 3 (2 \sqrt{2}) - \sqrt{2} (3 + 2 \sqrt{2})$

Step 2.3

Apply the distributive property.

$3 \cdot 3 + 3 (2 \sqrt{2}) - \sqrt{2} \cdot 3 - \sqrt{2} (2 \sqrt{2})$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $3$ by $3$ .

$9 + 3 (2 \sqrt{2}) - \sqrt{2} \cdot 3 - \sqrt{2} (2 \sqrt{2})$

Step 3.1.2

Multiply $2$ by $3$ .

$9 + 6 \sqrt{2} - \sqrt{2} \cdot 3 - \sqrt{2} (2 \sqrt{2})$

Step 3.1.3

Multiply $3$ by $- 1$ .

$9 + 6 \sqrt{2} - 3 \sqrt{2} - \sqrt{2} (2 \sqrt{2})$

Step 3.1.4

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

Tap for more steps...

Step 3.1.4.1

Multiply $2$ by $- 1$ .

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 \sqrt{2} \sqrt{2}$

Step 3.1.4.2

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

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 ({\sqrt{2}}^{1} \sqrt{2})$

Step 3.1.4.3

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

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 3.1.4.4

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

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 {\sqrt{2}}^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 {\sqrt{2}}^{2}$

Step 3.1.5

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

Tap for more steps...

Step 3.1.5.1

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

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 {(2^{\frac{1}{2}})}^{2}$

Step 3.1.5.2

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

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 3.1.5.3

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

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 \cdot 2^{\frac{2}{2}}$

Step 3.1.5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.5.4.1

Cancel the common factor.

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 \cdot 2^{\frac{2}{2}}$

Step 3.1.5.4.2

Rewrite the expression.

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 \cdot 2^{1}$

Step 3.1.5.5

Evaluate the exponent.

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 2 \cdot 2$

Step 3.1.6

Multiply $- 2$ by $2$ .

$9 + 6 \sqrt{2} - 3 \sqrt{2} - 4$

Step 3.2

Subtract $4$ from $9$ .

$5 + 6 \sqrt{2} - 3 \sqrt{2}$

Step 3.3

Subtract $3 \sqrt{2}$ from $6 \sqrt{2}$ .

$5 + 3 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 + 3 \sqrt{2}$

Decimal Form:

$9.24264068 \dots$