Root Eye

Algebra Level 1

Express 2 3 − 7 \dfrac{2}{3-\sqrt{7}} in form of a + b a+\sqrt{b} , where a a and b b are integers.

6 + 7 6+\sqrt 7 3 + 7 3+\sqrt 7 3 − 7 3-\sqrt 7 1 + 7 1+\sqrt 7

Olufemi Professor by olufemi professor , 21, Norway

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1 solution

Andy Wong
Sep 29, 2015

A good way to solve these types of problems is to multiply the numerator and denominator by the denominator's conjugate.

2 3 − 7 ( 3 + 7 3 + 7 ) = 2 ( 3 + 7 ) 9 − 7 = 2 ( 3 + 7 ) 2 = 3 + 7 \frac { 2 }{ 3-\sqrt { 7 } } \left( \frac { 3+\sqrt { 7 } }{ 3+\sqrt { 7 } } \right) \quad =\quad \frac { 2\left( 3+\sqrt { 7 } \right) }{ 9-7 } \quad =\quad \frac { 2\left( 3+\sqrt { 7 } \right) }{ 2 } \quad =\quad 3+\sqrt { 7 }

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