Cancelling out problem (2 different answers?) I am getting two different answers depending oh how I cancel out the numbers in the numerator and denominator. When I take (sqrt2/2)/(sqrt 2/2)^2, I would normally cancel out (sqrt 2/2) in both the numerator and denominator so I am left with 1/(sqrt 2/2). I would then multiply the numerator by the reciprocal to come to 2/sqrt 2

zaiskaladu

zaiskaladu

Answered question

2022-09-23

Cancelling out problem (2 different answers?)
I am getting two different answers depending oh how I cancel out the numbers in the numerator and denominator.
When I take ( 2 / 2 ) / ( 2 / 2 ) 2 , I would normally cancel out ( 2 / 2 ) in both the numerator and denominator so I am left with 1 / ( 2 / 2 ). I would then multiply the numerator by the reciprocal to come to 2 / 2
HOWEVER, when I take ( 2 / 2 ) / ( 2 / 2 ) 2 and multiply out the denominator, I get ( 2 / 2 ) / ( 2 / 4 ), I then multiply the numerator by the recipcrocal to get an answer of 2
I should get the same thing shouldn't I, where am I going wrong? Thanks for your help.

Answer & Explanation

Mario Dorsey

Mario Dorsey

Beginner2022-09-24Added 12 answers

In case you care to see it worked out...
2 2 = 2 2 2 2 = 2 2 2 = 2
I guess teachers call this "rationalizing the denominator" or something.
Daniella Reyes

Daniella Reyes

Beginner2022-09-25Added 3 answers

Using the fact that a n a m = a n + m or b n / b m = b n b m = b n m :
2 2 = 2 1 2 1 / 2 = 2 1 2 1 / 2 = 2 1 1 / 2 = 2 1 / 2 = 2
i.e. the algebra of exponents.

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