Simplify (10-3 square root of 2)/( square root of 2-1)

$\frac{10 - 3 \sqrt{2}}{\sqrt{2} - 1}$

Multiply $\frac{10 - 3 \sqrt{2}}{\sqrt{2} - 1}$ by $\frac{\sqrt{2} + 1}{\sqrt{2} + 1}$ .

$\frac{10 - 3 \sqrt{2}}{\sqrt{2} - 1} \cdot \frac{\sqrt{2} + 1}{\sqrt{2} + 1}$

Combine fractions.

Multiply $\frac{10 - 3 \sqrt{2}}{\sqrt{2} - 1}$ by $\frac{\sqrt{2} + 1}{\sqrt{2} + 1}$ .

$\frac{(10 - 3 \sqrt{2}) (\sqrt{2} + 1)}{(\sqrt{2} - 1) (\sqrt{2} + 1)}$

Expand the denominator using the FOIL method.

$\frac{(10 - 3 \sqrt{2}) (\sqrt{2} + 1)}{{\sqrt{2}}^{2} + \sqrt{2} - \sqrt{2} - 1}$

Simplify.

$\frac{(10 - 3 \sqrt{2}) (\sqrt{2} + 1)}{1}$

Divide $(10 - 3 \sqrt{2}) (\sqrt{2} + 1)$ by $1$ .

$(10 - 3 \sqrt{2}) (\sqrt{2} + 1)$

Expand $(10 - 3 \sqrt{2}) (\sqrt{2} + 1)$ using the FOIL Method.

Apply the distributive property.

$10 (\sqrt{2} + 1) - 3 \sqrt{2} (\sqrt{2} + 1)$

Apply the distributive property.

$10 \sqrt{2} + 10 \cdot 1 - 3 \sqrt{2} (\sqrt{2} + 1)$

Apply the distributive property.

$10 \sqrt{2} + 10 \cdot 1 - 3 \sqrt{2} \sqrt{2} - 3 \sqrt{2} \cdot 1$

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $1$ .

$10 \sqrt{2} + 10 - 3 \sqrt{2} \sqrt{2} - 3 \sqrt{2} \cdot 1$

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

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

$10 \sqrt{2} + 10 - 3 ({\sqrt{2}}^{1} \sqrt{2}) - 3 \sqrt{2} \cdot 1$

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

$10 \sqrt{2} + 10 - 3 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) - 3 \sqrt{2} \cdot 1$

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

$10 \sqrt{2} + 10 - 3 {\sqrt{2}}^{1 + 1} - 3 \sqrt{2} \cdot 1$

Add $1$ and $1$ .

$10 \sqrt{2} + 10 - 3 {\sqrt{2}}^{2} - 3 \sqrt{2} \cdot 1$

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

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

$10 \sqrt{2} + 10 - 3 {(2^{\frac{1}{2}})}^{2} - 3 \sqrt{2} \cdot 1$

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

$10 \sqrt{2} + 10 - 3 \cdot 2^{\frac{1}{2} \cdot 2} - 3 \sqrt{2} \cdot 1$

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

$10 \sqrt{2} + 10 - 3 \cdot 2^{\frac{2}{2}} - 3 \sqrt{2} \cdot 1$

Cancel the common factor of $2$ .

Cancel the common factor.

$10 \sqrt{2} + 10 - 3 \cdot 2^{\frac{2}{2}} - 3 \sqrt{2} \cdot 1$

Rewrite the expression.

$10 \sqrt{2} + 10 - 3 \cdot 2^{1} - 3 \sqrt{2} \cdot 1$

Evaluate the exponent.

$10 \sqrt{2} + 10 - 3 \cdot 2 - 3 \sqrt{2} \cdot 1$

Multiply $- 3$ by $2$ .

$10 \sqrt{2} + 10 - 6 - 3 \sqrt{2} \cdot 1$

Multiply $- 3$ by $1$ .

$10 \sqrt{2} + 10 - 6 - 3 \sqrt{2}$

Subtract $3 \sqrt{2}$ from $10 \sqrt{2}$ .

$10 - 6 + 7 \sqrt{2}$

Subtract $6$ from $10$ .

$4 + 7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$4 + 7 \sqrt{2}$

Decimal Form:

$13.89949493 \dots$

Simplify (10-3 square root of 2)/( square root of 2-1)

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