What is (sqrt(5)-1)/(sqrt(10)-\sqrt{2)} ?

The solution to (sqrt(5)-1)/(sqrt(10)-\sqrt{2)} is 1/(sqrt(2))

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simplify (sqrt(5)-1)/(sqrt(10)-\sqrt{2)}

simplify

\frac{5 - 1}{10 - 2}

\frac{1}{2}

Decimal Notation

0.70710 \dots

Solution steps

\frac{5 - 1}{10 - 2}

Multiply by the conjugate

\frac{10 + 2}{10 + 2}

= \frac{( 5 - 1 ) ( 10 + 2 )}{( 10 - 2 ) ( 10 + 2 )}

Expand

(5 - 1) (10 + 2) : 42

Expand

(10 - 2) (10 + 2) : 8

= \frac{4 2}{8}

Factor the number:

8 = 4 \cdot 2

= \frac{4 2}{4 \cdot 2}

Cancel the common factor:

4

= \frac{2}{2}

Apply radical rule:

a = a a

2 = 22

= \frac{2}{2 2}

Cancel the common factor:

2

= \frac{1}{2}

h - 6 + 7 h = 42

36 = 4 c

3 x + 2 > - x - 14

∣ x - 4 ∣ + 12 = 29

5 (x - 2) \leq 0 and - 3 x > 9

What is (sqrt(5)-1)/(sqrt(10)-\sqrt{2)} ?
The solution to (sqrt(5)-1)/(sqrt(10)-\sqrt{2)} is 1/(sqrt(2))