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
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
if `x = 2 + sqrt3`,find the value of `x^2 + 1/x^2`
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
