Advertisements
Advertisements
प्रश्न
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Advertisements
उत्तर
We know that rationalization factor for `5sqrt3 - 3sqrt5` is `5sqrt3 + 3sqrt5`. We will multiply numerator and denominator of the given expression `30/(5sqrt3 - 3sqrt5)` by `5sqrt3 + 3sqrt5` to get
`30/(5sqrt3 - 3sqrt5) xx (5sqrt3 + 3sqrt5)/(5sqrt3 + 3sqrt5)`
= `(30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/(5(sqrt3)^2 - (3sqrt3)^2)`
`= (30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/(25 xx 3 - 9 xx 5)`
`= (30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/30`
`(150sqrt3 + 90sqrt5)/30`
`(150sqrt3)/30 + (90sqrt5)/30`
`= 5sqrt3 + 3sqrt5`
APPEARS IN
संबंधित प्रश्न
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of x and y.
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Rationalise the denominator of the following:
`2/(3sqrt(3)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - 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.
`sqrt(2)/(2 + sqrt(2)`
