Advertisements
Advertisements
प्रश्न
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Advertisements
उत्तर
We know that rationalization factor for `sqrt6 - sqrt5` is `sqrt6 + sqrt5`. We will multiply numerator and denominator of the given expression `1/(sqrt6 -sqrt5)` by `sqrt6 + sqrt5` to get
`1/(sqrt6 - sqrt5) xx (sqrt6 + sqrt5)/(sqrt6 + sqrt5) = (sqrt6 + sqrt6)/((sqrt6)^2 - (sqrt5)^2`
`= (sqrt6 + sqrt5)/(6 - 5)`
`= (sqrt6 + sqrt5)/(6 - 5)`
`= (sqrt6 + sqrt5)/1`
`= sqrt6 + sqrt5`
Hence the given expression is simplified with rational denominator to `sqrt6 + sqrt5`.
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
Rationalise the denominator of each of the following
`1/sqrt12`
Express the following with rational denominator:
`16/(sqrt41 - 5)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
Simplify the following:
`(2sqrt(3))/3 - sqrt(3)/6`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - 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.
`6/sqrt(6)`
