Advertisements
Advertisements
Question
Rationalise the denominator:
`(sqrt(5) + 2)/(sqrt(5) - 2)`
Sum
Advertisements
Solution
We are asked to rationalise:
`(sqrt(5) + 2)/(sqrt(5) - 2)`
Step 1: Multiply numerator and denominator by the conjugate of the denominator:
`(sqrt(5) + 2)/(sqrt(5) - 2) xx (sqrt(5) + 2)/(sqrt(5) + 2) = (sqrt(5) + 2)^2/((sqrt(5))^2 - 2^2)`
Step 2: Simplify numerator:
`(sqrt(5) + 2)^2`
= `(sqrt(5))^2 + 2 xx sqrt(5) xx 2 + 2^2`
= `5 + 4sqrt(5) + 4`
= `9 + 4sqrt(5)`
Step 3: Simplify denominator:
`(sqrt(5))^2 - (2)^2`
= 5 – 4
= 1
`(9 + 4sqrt(5))/1`
= `9 + 4sqrt(5)`
shaalaa.com
Is there an error in this question or solution?
Chapter 1: Rational and Irrational Numbers - MISCELLANEOUS EXERCISE [Page 17]
