Advertisements
Advertisements
प्रश्न
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Advertisements
उत्तर
We know that rationalization factor for `3sqrt2 +2sqrt3` and `sqrt3-sqrt2`are `3sqrt2 - 2sqrt3`and `sqrt3 +sqrt2`respectively. We will multiply numerator and denominator of the given expression `(3sqrt2 -2sqrt3)/ (3sqrt2 +2sqrt3)` and `sqrt12/(sqrt3-sqrt2)`by `3sqrt2-2sqrt3`and `sqrt3 +sqrt2`respectively, to get
`(3sqrt2 -2sqrt3)/ (3sqrt2 +2sqrt3) xx (3sqrt2 -2sqrt3)/ (3sqrt2 -2sqrt3) +sqrt12/(sqrt3-sqrt2) xx (sqrt3 +sqrt2)/(sqrt3 +sqrt2) =((3sqrt2)^2+(2sqrt3)^2 - 2xx 3 sqrt2 xx 2sqrt3)/((3sqrt2)^2 -( 2sqrt3)^2 ) +(sqrt36+sqrt24)/((sqrt3)^2-(sqrt2)^2)`
`= (18+12-12sqrt6)/(18-12) +(6+sqrt24)/(3-2)`
`= (30-12sqrt6 +36 +12sqrt6)/6`
`=66/6`
`=11`
APPEARS IN
संबंधित प्रश्न
Simplify the following expression:
`(3+sqrt3)(2+sqrt2)`
Rationalise the denominator of the following:
`1/sqrt7`
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Value of (256)0.16 × (256)0.09 is ______.
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
