4/(sqrt 2 + 3) #rationalize the denominators

Question

4/(sqrt 2 + 3) #rationalize the denominators

 

Answer 1

OK, I ASSUME YOU MEAN

 

4 / (SQRT(2) + 3)    CORRECT ??

 

IF SO, TO RATIONALIZE WE NEED TO REMOVE THE SQRT FROM THE DENOM. 

 

WE DO THAT BY MULTIPLYING NUMBERATOR AND DENOMINATOR BY  THE CONJUGATE

 

THE CONJUGATE IS USING THE OPPOSITE SIGN ON THE SUM OR DIFF. 

 

SO THE CONJUGATE OF (SQRT(2) + 3)  IS (SQRT(2) - 3). 

NOW, YOU'LL SEE WHAT THAT DOES  TO THE DENOMINATOR

 

[4 / (SQRT(2) + 3) ]   *  [( SQRT(2) - 3) / (SQRT(2) - 3) ] 

 

SO 4*[SQRT(2) - 3] /  [2  + 3*SQRT(2) - 3*SQRT(2) - 9]

 

NOTE THE 3*SQRT(2)  AND - 3*SQRT(2) CANCEL AND THE DENOM IS JUST 2 -9 = -7 

 

[4*SQRT(2) - 12] / [-7]    

 

THIS IS =   [12 - 4*SQRT(2)] / 7  IF WE MULT BY -1/-1

Answer 2

Hello Lauren,

 

Because (a-b)(a+b)=a^2-b^2, if it is 4/(sqrt(2)+3). To rationalize the denominator, you need to multiply the fraction by (sqrt(2)-3)/(sqrt(2)-3) so that the denominator becomes 2-9 = 7.

 

And since you multiply sqrt(2)-3 to the numerator as well, you now have 4(sqrt(2)-3) or 4sqrt(2)-12 as your numerator.