Simplify -8/(3+ square root of 17)

$\frac{- 8}{3 + \sqrt{17}}$

Step 1

Move the negative in front of the fraction.

$- \frac{8}{3 + \sqrt{17}}$

Step 2

Multiply $\frac{8}{3 + \sqrt{17}}$ by $\frac{3 - \sqrt{17}}{3 - \sqrt{17}}$ .

$- (\frac{8}{3 + \sqrt{17}} \cdot \frac{3 - \sqrt{17}}{3 - \sqrt{17}})$

Step 3

Multiply $\frac{8}{3 + \sqrt{17}}$ by $\frac{3 - \sqrt{17}}{3 - \sqrt{17}}$ .

$- \frac{8 (3 - \sqrt{17})}{(3 + \sqrt{17}) (3 - \sqrt{17})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{8 (3 - \sqrt{17})}{9 - 3 \sqrt{17} + \sqrt{17} \cdot 3 - {\sqrt{17}}^{2}}$

Step 5

Simplify.

$- \frac{8 (3 - \sqrt{17})}{- 8}$

Step 6

Simplify the expression.

Move the negative one from the denominator of $\frac{3 - \sqrt{17}}{- 1}$ .

$- (- 1 \cdot (3 - \sqrt{17}))$

Rewrite $- 1 \cdot (3 - \sqrt{17})$ as $- (3 - \sqrt{17})$ .

$- - (3 - \sqrt{17})$

Step 7

Apply the distributive property.

$- (- 1 \cdot 3 - - \sqrt{17})$

Step 8

Multiply $- 1$ by $3$ .

$- (- 3 - - \sqrt{17})$

Step 9

Multiply $- - \sqrt{17}$ .

Multiply $- 1$ by $- 1$ .

$- (- 3 + 1 \sqrt{17})$

Multiply $\sqrt{17}$ by $1$ .

$- (- 3 + \sqrt{17})$

Step 10

Apply the distributive property.

$- - 3 - \sqrt{17}$

Step 11

Multiply $- 1$ by $- 3$ .

$3 - \sqrt{17}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$3 - \sqrt{17}$

Decimal Form:

$- 1.12310562 \dots$

Simplify -8/(3+ square root of 17)

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