Advertisements
Advertisements
प्रश्न
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Advertisements
उत्तर
We know that rationalization factor for `6 + 4sqrt2` is `6 - 4sqrt2`. We will multiply numerator and denominator of the given expression `(6 - 4sqrt2)/(6 + 4sqrt2)` by `6 - 4sqrt2` to get
`(6 - 4sqrt2)/(6 + 4sqrt2) xx (6 - 4sqrt2)/(6 - 4sqrt2) = (6^2 + (4sqrt2)^2 - 2 xx 6 4 sqrt2)/((6)^2 - (4sqrt2)^2)`
` (36 + 16 xx 2 - 48sqrt2)/(36 - 16 xx 2)`
`= (36 + 32 - 48sqrt2)/(36 - 32)`
`= (68 - 48sqrt2)/4`
`= 17 - 12sqrt2`
Hence the given expression is simplified with rational denominator to `17 - 12sqrt2`
APPEARS IN
संबंधित प्रश्न
Rationalise the denominator of the following:
`1/sqrt7`
Simplify of the following:
`root(3)4 xx root(3)16`
Simplify of the following:
`root(4)1250/root(4)2`
Rationales the denominator and simplify:
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Classify the following number as rational or irrational:
`(3+sqrt23)-sqrt23`
Rationalise the denominator of the following:
`2/(3sqrt(3)`
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.
`6/sqrt(6)`
