Advertisements
Advertisements
प्रश्न
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(3 - sqrt5)/(3 + 2sqrt5)`
Advertisements
उत्तर
We know that rationalization factor for `3 + 2sqrt5` is `3 - sqrt5`. We will multiply numerator and denominator of the given expression `(3 - sqrt5)/(3 + 2sqrt5)` by `3 - 2sqrt5` to get
`(3 - sqrt5)/(3 + 2sqrt5) xx (3 - 2sqrt5)/(3 - 2sqrt5) = ((3)^2 - 3 xx 2 xx sqrt5 - 3 xx sqrt5 + 2 xx (sqrt5)^2)/((3)^2 - (2sqrt5)^2)`
` = (9 - 9sqrt5 + 10)/(9 - 20)`
`= (19 - 9sqrt5)/(-11)`
`= (9sqrt5 - 19)/11`
Putting the value of `sqrt5`, we get
`(9sqrt5 - 19)/11 = (9(2.236) - 19)/11`
`= (20.124 - 19)/11`
`= 1.124/11`
= 0.102
Hence the given expression is simplified to 0.102
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Write the reciprocal of \[5 + \sqrt{2}\].
Classify the following number as rational or irrational:
2π
Simplify the following expression:
`(sqrt5+sqrt2)^2`
Rationalise the denominator of the following:
`1/(sqrt7-2)`
