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प्रश्न
Rationales the denominator and simplify:
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`
उत्तर
We know that rationalization factor for `sqrt48 + sqrt18` is `sqrt48 - sqrt18`. We will multiply numerator and denominator of the given expression `(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)` by `sqrt48 - sqrt18` to get
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18) xx (sqrt48 - sqrt18)/(sqrt48 - sqrt18) = (4 xx sqrt3 xx sqrt48 - 4 sqrt3 xx sqrt18 + 5 xx sqrt2 xx sqrt48 - 5 xx sqrt2 xx sqrt18)/((sqrt48)^2 - (sqrt18)^2)`
` = (4sqrt(3 xx 48) - 4 xx sqrt(3 xx 18) + 5 xx sqrt(2 xx 48) - 5 xx sqrt(2 xx 18))/(48 - 18)`
`= (4sqrt144 - 4sqrt54 + 5sqrt(96) - 5sqrt36)/30`
`= (4 xx 12 - 4 xx sqrt9 xx sqrt6 + 5 xx sqrt16 xx sqrt6 - 5sqrt36)/30`
`= (48 - 4 xx 3 xx sqrt6 + 5 xx 4 xx sqrt6 - 5 xx 6)/30`
`= (48 - 12sqrt6 + 20sqrt6 - 30)/30`
`= (18 + 8sqrt6)/30`
`= (9 + 4sqrt6)/15`
Hence the given expression is simplified to `(9 + 4sqrt6)/15`
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संबंधित प्रश्न
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Express the following with rational denominator:
`1/(3 + sqrt2)`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Write the rationalisation factor of \[\sqrt{5} - 2\].
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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)`
