Advertisements
Advertisements
प्रश्न
Express the following with rational denominator:
`1/(3 + sqrt2)`
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 the following expressions:
`(11 + sqrt11)(11 - sqrt11)`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of x and y.
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
Value of (256)0.16 × (256)0.09 is ______.
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)`
