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प्रश्न
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
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उत्तर
We know that rationalization factor for `4 - 3sqrt5` is `4 + 3sqrt5`. We will multiply numerator and denominator of the given expression `(4 + 3sqrt5)/(3 - 3sqrt5)` by `4 + 3sqrt5` to get
`(4 + 3sqrt5)/(4 - 3sqrt5) xx (4 + 3sqrt5)/(4 + 3sqrt5) = ((4)^2 + (3sqrt3)^2 + 2 xx 4 xx 3sqrt5)/((4)^2 - (3sqrt5)^2)`
`= (16 + 45 + 24sqrt5)/(16 - 45)`
`= (61 + 24sqrt5)/(-29)`
`= -61/29 - 24/29 sqrt5`
On equating rational and irrational terms, we get
`a + bsqrt5 = -61/29 - 24/29 sqrt5`
Hence we get `a = -61/29, b = -24/29`
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संबंधित प्रश्न
Classify the following numbers as rational or irrational:
`2-sqrt5`
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`(sqrt2 + sqrt5)/3`
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`(3 - sqrt5)/(3 + 2sqrt5)`
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
Simplify:
`64^(-1/3)[64^(1/3) - 64^(2/3)]`
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
