Advertisements
Advertisements
Question
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Advertisements
Solution
We know that rationalization factor for `sqrt3 + sqrt2` is "sqrt3 - sqrt2". We will multiply numerator and denominator of the given expression `(sqrt3 - sqrt2)/(sqrt3 + sqrt2)` by `sqrt3 - sqrt2` to get
`(sqrt3 - sqrt2)/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) = ((sqrt3)^2 + (sqrt2)^2 - 2 sqrt3 xx sqrt2)/((sqrt3)^2 - (sqrt2)^2)`
`= (3 + 2 - 2sqrt6)/(3 - 2)`
`= (5 - 2sqrt6)/1`
`= 5 - 2sqrt6`
Hence the given expression is simplified to `5 - 2sqrt6`
APPEARS IN
RELATED QUESTIONS
Classify the following numbers as rational or irrational:
`2-sqrt5`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
if `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Write the reciprocal of \[5 + \sqrt{2}\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
