Advertisements
Advertisements
प्रश्न
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
Advertisements
उत्तर
We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2`
`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2sqrt2 + 3sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`
` = (3 + 5sqrt2 + 4)/(9 - 4 xx 2)`
`= (7 + 5sqrt2)/(9 - 8)`
`= (7 + 5sqrt2)/1`
`= 7 + 5sqrt2`
Hence the given expression is simplified to `7 + 5sqrt2`
APPEARS IN
संबंधित प्रश्न
Simplify of the following:
`root(3)4 xx root(3)16`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
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`
`2/sqrt3`
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`
`(sqrt10 + sqrt15)/sqrt2`
`
Express the following with rational denominator:
`1/(3 + sqrt2)`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
