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प्रश्न
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
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उत्तर
We know that rationalization factor for `sqrt5 - sqrt3` is `sqrt5 + sqrt3`. We will multiply denominator and numerator of the given expression `6/(sqrt5 - sqrt3)` by `sqrt5 + sqrt3` to get
`6/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) = (6sqrt5 + 6sqrt3)/((sqrt5)^2 - (sqrt3)^3)`
`= (6sqrt5 + 6sqrt3)/(5 - 3)`
`= (6sqrt5 + 6sqrt3)/2`
`= 3sqrt5 + 3sqrt3`
Putting the values of `sqrt5` and `sqrt3` we get
`3sqrt5 + 3sqrt3 = 3(2.236) + 3(1.732)`
= 6.708 + 5.196
= 11.904
Hence value of the given expression is 11.904
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संबंधित प्रश्न
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?
Simplify the following expressions:
`(11 + sqrt11)(11 - sqrt11)`
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Rationalise the denominator of each of the following
`3/sqrt5`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`3/sqrt10`
Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Simplify:
`(1/27)^((-2)/3)`
