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प्रश्न
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
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उत्तर
Let `E = sqrt(6)/(sqrt(2) + sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(2) - sqrt(3)`,
`E = sqrt(6)/(sqrt(2) + sqrt(3)) xx (sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))`
= `(sqrt(6)(sqrt(2) - sqrt(3)))/((sqrt(2))^2 - (sqrt(3))^2)` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `(sqrt(6) (sqrt(2) - sqrt(3)))/(2 - 3)`
= `(sqrt(6)(sqrt(2) - sqrt(3)))/(-1)`
= `sqrt(6)(sqrt(3) - sqrt(2))`
= `sqrt(18) - sqrt(12)`
= `sqrt(9 xx 2) - sqrt(4 xx 3)`
= `3sqrt(2) - 2sqrt(3)`
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संबंधित प्रश्न
Rationalise the denominator of each of the following
`3/sqrt5`
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)`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
Classify the following number as rational or irrational:
`1/sqrt2`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
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.
`4/sqrt(3)`
