Rationalization 101

Algebra Level 2

Rationalize the denominator and simplify: 2 2 6 + 2 \frac{2\sqrt{2}}{\sqrt{6} +\sqrt{2}}

3 \sqrt{3} - 1 4 \sqrt{4} - 2 4 \sqrt{4} - 5 2 \sqrt{2} + 1

Jax Lincoln by Jax Lincoln , 19, Philippines

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1 solution

Jax Lincoln
Oct 15, 2017

2 2 6 + 2 \frac{2\sqrt{2}}{\sqrt{6} +\sqrt{2}} = 2 2 2 ( 3 + 1 ) \frac{2\sqrt{2}}{\sqrt{2}(\sqrt{3} +1)}

= 2 ( 3 + 1 ) \frac{2}{(\sqrt{3} +1)} × \times 3 − 1 3 − 1 \frac{\sqrt{3}-1}{\sqrt{3}-1}

= 2 ( 3 − 1 ) 3 − 1 \frac{2(\sqrt{3}-1)}{\sqrt{3}-1}

= 3 − 1 \sqrt{3}-1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Hey you elton wtf!!!

A Former Brilliant Member - 3 years, 7 months ago

In the third step you wrongly typed it as 3 − 1 \sqrt{3} - 1 . actually it should be 3 − 1 = 2 3 -1 = 2 or 3 2 − 1 2 = 3 − 1 = 2 \sqrt{3}^2 - 1^2 = 3-1 = 2

Ram Mohith - 3 years, 1 month ago

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