What is 3/(sqrt(17)-\sqrt{2)} ?

The solution to 3/(sqrt(17)-\sqrt{2)} is (sqrt(17)+sqrt(2))/5

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simplify 3/(sqrt(17)-\sqrt{2)}

simplify

\frac{3}{17 - 2}

\frac{17 + 2}{5}

Decimal Notation

1.10746 \dots

Solution steps

\frac{3}{17 - 2}

Multiply by the conjugate

\frac{17 + 2}{17 + 2}

= \frac{3 ( 17 + 2 )}{( 17 - 2 ) ( 17 + 2 )}

Expand

3 (17 + 2) : 317 + 32

Expand

(17 - 2) (17 + 2) : 15

= \frac{3 17 + 3 2}{15}

Factor out common term

3

= \frac{3 ( 17 + 2 )}{15}

Factor the number:

15 = 3 \cdot 5

= \frac{3 ( 17 + 2 )}{3 \cdot 5}

Cancel the common factor:

3

= \frac{17 + 2}{5}

5 \cdot \frac{7}{3}

1000000 (1 + 0.02)^{5}

8 - ∣ - 6 ∣ + 3

(\frac{p ^{3}}{q ^{2}})^{- 3}

(- 6 ab) (0.5 a c)

What is 3/(sqrt(17)-\sqrt{2)} ?
The solution to 3/(sqrt(17)-\sqrt{2)} is (sqrt(17)+sqrt(2))/5