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प्रश्न
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
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उत्तर
We know that rationalization factor for `7 + 4sqrt3` is `7 - 4sqrt3`. We will multiply numerator and denominator of the given expression `(5 + 2sqrt3)/(7 + 4sqrt3)` by `7 - 4sqrt3` to get
`(5 + 2sqrt3)/(7 + 4sqrt3) xx (7 - 4sqrt3)/(7 - 4sqrt3) = (5xx7 - 5 xx 4sqrt3 + 2 xx 7 xx sqrt3 - 2 xx 4 xx (sqrt3)^2)/((7)^2 - (4sqrt3)^2)`
`= (35 - 20sqrt3 + 14sqrt3 - 8 xx 3)/(49 - 49)`
`= (11 - 6sqrt3)/1`
`= 11 - 6sqrt3`
Hence the given expression is simplified to `11 - 6sqrt3`
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संबंधित प्रश्न
Classify the following numbers as rational or irrational:
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Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
The value of `(sqrt(32) + sqrt(48))/(sqrt(8) + sqrt(12))` is equal to ______.
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
