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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:
`2-sqrt5`
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
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`root(3)4 xx root(3)16`
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Find the value of a and b in the following:
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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.
`6/sqrt(6)`
