How do you simplify (2sqrt 8 + 7sqrt8)/(1 - sqrt2)?

2 Answers
Gió
Apr 15, 2015

We can add the terms in the numerator and then rationalize:
(9sqrt(8))/(1-sqrt(2))*(1+sqrt(2))/(1+sqrt(2))=
=(9sqrt(8)(1+sqrt(2)))/(1-2)=
=-9sqrt(4*2)(1+sqrt(2))=
=-18sqrt(2)(1+sqrt(2))

Alan P.
Apr 15, 2015
  1. Simplify the numerator.
  2. Multiply the numerator and denominator by the conjugate of the denominator.
  3. Simplify a bit more.

Step 1
2sqrt(8)+7sqrt(8)
= 9sqrt(8)
=9sqrt(2^*2)
=18sqrt(2)

Step2
(18sqrt(2))/(1-sqrt(2)) * (1+sqrt(2))/(1+sqrt(2))

= (18sqrt(2)+36)/(1-(sqrt(2)^2)

Step 3
= - (36+18sqrt(2))

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