How do you rationalize the denominator and simplify 12√5−1?

2 Answers
KillerBunny
May 28, 2018

3(√5+1)

Explanation:

Use the identities

  • aa=1 for every non-zero a
  • (a+b)(a−b)=a2−b2

to write

12√5−1=12√5−1⋅1=12√5−1=12√5−1⋅√5+1√5+1

Now, as you can see, the numerator is 12(√5+1), which is fine because we are allowed to have roots in the numerator.

The denominator, instead, is written in the same form as the second property written at the beginning:

(√5+1)(√5−1)=(√5)2+12=5−1=4

So, the fraction becomes

12(√5+1)4=3(√5+1)

Brandon
May 28, 2018

3√5+3

Explanation:

When having a root on the bottom with an extra + or − on the bottom, we multiply by the opposite:

⇒12√5−1×√5+1√5+1

⇒12√5+124

⇒3√5+3

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