Advertisements
Advertisements
Question
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`
`(1 + sqrt2)/(3 - 2sqrt2)`
Advertisements
Solution
We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2` to get
`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2 xx sqrt2 + 3 xx sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`
`= (3 + 2sqrt2 + 3sqrt2 + 4)/(9 - 8)`
`= (7 + 5sqrt2)/1`
Putting te value of `sqrt2` we get
`7 + 5sqrt2 = 7 + 5(1.4142)`
= 7 + 7.071
= 14.071
Hence the given expression is simplified to 14.071
APPEARS IN
RELATED QUESTIONS
Simplify of the following:
`root(4)1250/root(4)2`
Simplify the following expressions:
`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Rationalise the denominator of the following:
`1/(sqrt7-2)`
`1/(sqrt(9) - sqrt(8))` is equal to ______.
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
