Advertisements
Advertisements
Question
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
Advertisements
Solution
`1/(sqrta + sqrtb) xx ((sqrta - sqrtb)/(sqrta - sqrtb)) = (sqrta - sqrtb)/(a - b)`
`{1/(sqrta + sqrtb) = (sqrta - sqrtb)/(a - b)}`
= `2/1 ((sqrt5 - sqrt3)/(5 - 3)) + ((sqrt3 - sqrt2)/(3-2)) - (3/1)((sqrt5 - sqrt2)/(5 - 2))`
= `cancel2 xx (sqrt5 - sqrt3)/cancel2 + (sqrt3 - sqrt2)/1 = cancel3 xx (sqrt5 - sqrt2)/cancel3`
= `cancelsqrt5 - cancelsqrt3 + cancelsqrt3 - cancelsqrt2 - cancelsqrt5 + cancelsqrt2`
= 0
APPEARS IN
RELATED QUESTIONS
Rationalise the denominator of each of the following
`1/sqrt12`
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`
`(sqrt2 - 1)/sqrt5`
Write the reciprocal of \[5 + \sqrt{2}\].
Write the rationalisation factor of \[\sqrt{5} - 2\].
If \[x = 3 + 2\sqrt{2}\],then find the value of \[\sqrt{x} - \frac{1}{\sqrt{x}}\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Simplify the following:
`(2sqrt(3))/3 - sqrt(3)/6`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
