Advertisements
Advertisements
Question
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Advertisements
Solution
Let `E = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(3) + sqrt(2)`,
`E = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2)) xx (sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`
= `(sqrt(3) + sqrt(2))^2/((sqrt(3))^2 - (sqrt(2))^2` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `((sqrt(3))^2 + (sqrt(2))^2 + 2sqrt(3)sqrt(2))/(3 - 2)` ...[Using identity, (a + b)2 = a2 + b2 + 2ab]
= `3 + 2 + 2sqrt(6)`
= `5 + 2sqrt(6)`
APPEARS IN
RELATED QUESTIONS
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`3/sqrt10`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Value of (256)0.16 × (256)0.09 is ______.
Simplify the following:
`4sqrt12 xx 7sqrt6`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`6/sqrt(6)`
