How do you rationalize the denominator and simplify 12−2√68−5√2?

1 Answer
Tony B
Feb 12, 2017

See the explanation

Explanation:

Preamble

There is a trick to this. Apart from anything else, mathematicians do not like 'roots' in the denominator. It is considered good practice to 'get rid of them'.

The trick: multiply by its self but change the sign in the middle (for the second variable) .

Why? Consider: (a−b)(a+b)=a2−b2

Observe that everything ends up being squared. So any square roots disappear.
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Answering the question

12−2√68−5√2×1 = 12−2√68−5√2×8+5√28+5√2

=(12−2√6)(8+5√2)82−(5√2)2

=96+60√2−64√6−10√1264−50
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Consider 10√12→10√22×3=20√3
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=96+60√2−64√6−20√314

=48+30√2−32√6−5√127

I will leave the rest for you to do

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