Advertisements
Advertisements
Question
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
Advertisements
Solution
The given number is `1/(sqrt7 - sqrt6)`
On rationalising the denominator,
⇒ `1/(sqrt7 - sqrt6) = 1/(sqrt7 - sqrt6) xx (sqrt7 + sqrt6)/(sqrt7 + sqrt6)`
We know that (a + b) (a + b) = a2 - b2
⇒ `1/(sqrt7 - sqrt6) = (sqrt7 + sqrt6)/((sqrt7)^2 - (sqrt6)^2)`
⇒ `1/(sqrt7 - sqrt6) = (sqrt7 + sqrt6)/(7 - 6)`
∴ `1/(sqrt7 - sqrt6) = sqrt7 + sqrt6`
APPEARS IN
RELATED QUESTIONS
Express the following with rational denominator:
`16/(sqrt41 - 5)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
Classify the following number as rational or irrational:
`1/sqrt2`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
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.
`1/(sqrt(3) + sqrt(2))`
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
Simplify:
`(256)^(-(4^((-3)/2))`
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
