Advertisements
Advertisements
Question
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Advertisements
Solution
We have, `(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
For rationalising the above equation, we multiply numerator and denominator of LHS by `7 - 4sqrt(3)`, we get
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3)) = a - 6sqrt(3)`
`(5(7 - 4sqrt(3)) + 2sqrt(3)(7 - 4sqrt(3)))/(7^2 - (4sqrt(3))^2) = a - 6sqrt(3)` ...[Using identity, (a + b)(a – b) = a2 – b2]
⇒ `(35 - 20sqrt(3) + 14sqrt(3) - 24)/(49 - 48) = a - 6sqrt(3)`
⇒ `11 - 6sqrt(3) = a - 6sqrt(3) = a` = 11
APPEARS IN
RELATED QUESTIONS
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Rationalise the denominator of each of the following
`3/sqrt5`
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Write the rationalisation factor of \[\sqrt{5} - 2\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
