Simplify square root of 18(5- square root of 2)-11 square root of 2

$\sqrt{18} (5 - \sqrt{2}) - 11 \sqrt{2}$

Step 1

Simplify each term.

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

Factor $9$ out of $18$ .

$\sqrt{9 (2)} (5 - \sqrt{2}) - 11 \sqrt{2}$

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

$\sqrt{3^{2} \cdot 2} (5 - \sqrt{2}) - 11 \sqrt{2}$

Pull terms out from under the radical.

$3 \sqrt{2} (5 - \sqrt{2}) - 11 \sqrt{2}$

Apply the distributive property.

$3 \sqrt{2} \cdot 5 + 3 \sqrt{2} (- \sqrt{2}) - 11 \sqrt{2}$

Multiply $5$ by $3$ .

$15 \sqrt{2} + 3 \sqrt{2} (- \sqrt{2}) - 11 \sqrt{2}$

Multiply $3 \sqrt{2} (- \sqrt{2})$ .

Multiply $- 1$ by $3$ .

$15 \sqrt{2} - 3 \sqrt{2} \sqrt{2} - 11 \sqrt{2}$

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

$15 \sqrt{2} - 3 ({\sqrt{2}}^{1} \sqrt{2}) - 11 \sqrt{2}$

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

$15 \sqrt{2} - 3 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) - 11 \sqrt{2}$

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

$15 \sqrt{2} - 3 {\sqrt{2}}^{1 + 1} - 11 \sqrt{2}$

Add $1$ and $1$ .

$15 \sqrt{2} - 3 {\sqrt{2}}^{2} - 11 \sqrt{2}$

Simplify each term.

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

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

$15 \sqrt{2} - 3 {(2^{\frac{1}{2}})}^{2} - 11 \sqrt{2}$

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

$15 \sqrt{2} - 3 \cdot 2^{\frac{1}{2} \cdot 2} - 11 \sqrt{2}$

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

$15 \sqrt{2} - 3 \cdot 2^{\frac{2}{2}} - 11 \sqrt{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$15 \sqrt{2} - 3 \cdot 2^{\frac{2}{2}} - 11 \sqrt{2}$

Rewrite the expression.

$15 \sqrt{2} - 3 \cdot 2^{1} - 11 \sqrt{2}$

Evaluate the exponent.

$15 \sqrt{2} - 3 \cdot 2 - 11 \sqrt{2}$

Multiply $- 3$ by $2$ .

$15 \sqrt{2} - 6 - 11 \sqrt{2}$

Step 2

Subtract $11 \sqrt{2}$ from $15 \sqrt{2}$ .

$- 6 + 4 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 6 + 4 \sqrt{2}$

Decimal Form:

$- 0.34314575 \dots$

Simplify square root of 18(5- square root of 2)-11 square root of 2

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