How can I get rid of the square roots in this fraction?

sqrt((2-sqrt3))/sqrt((2+sqrt3))

the answer is 2-sqrt3

but I don't know how they arrive at it.

1 answer

Multiply both the numerator and denominator by the conjugate, sqrt((2-sqrt3))
Then
sqrt(2-sqrt3)/sqrt(2+sqrt3)
=sqrt(2-sqrt3)sqrt(2-sqrt3)/(sqrt(2+sqrt3)sqrt(2-sqrt3))
=sqrt((2-sqrt3)²)/sqrt(2²-3)
=(2-sqrt(3))/sqrt(4-1)
=(2-sqrt(3))/sqrt(1)
=2-sqrt(3)
Similar Questions
    1. answers icon 1 answer
    1. answers icon 1 answer
  1. Multiplying sq rtssqrt18a^7b times sqrt27a^8b^6 Jake 1214- 18 = 9 * 2 then sqrt 18 = 3sqrt2 sqrt a^7 = a^3 * sqrt a 27 = 9 * 3
    1. answers icon 1 answer
  2. Find the exact solution(s) of the system: x^2/4-y^2=1 and x=y^2+1A)(4,sqrt3),(4,-sqrt3),(-4,sqrt3),(-4,-sqrt3)
    1. answers icon 0 answers
more similar questions