Advertisements
Advertisements
प्रश्न
Express the following with rational denominator:
`1/(3 + sqrt2)`
Advertisements
उत्तर
We know that rationalization factor for `3 + sqrt2` is `3 - sqrt2`. We will multiply numerator and denominator of the given expression `1/(3 + sqrt2)` by `3 - sqrt2` to get
`1/(3 + sqrt2) xx (3 - sqrt2)/(3 - sqrt2) = (3 - sqrt2)/(3^2 - (sqrt2)^2)`
`= (3 - sqrt2)/(9 - 2)`
`= (3 - sqrt2)/7`
Hence the given expression is simplified with rational denominator to `(3 - sqrt2)/7`
APPEARS IN
संबंधित प्रश्न
Simplify of the following:
`root(4)1250/root(4)2`
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Rationalise the denominator of each of the following
`1/sqrt12`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Express the following with rational denominator:
`16/(sqrt41 - 5)`
In the following determine rational numbers a and b:
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
