Advertisements
Advertisements
Question
Given `sqrt(2)` = 1.414, find the value of `(8 - 5sqrt(2))/(3 - 2sqrt(2))` (to 3 places of decimals).
Advertisements
Solution
`(8 - 5sqrt(2))/(3 - 2sqrt(2)) = ((8 - 5sqrt(2))(3 + 2sqrt(2)))/((3 - 2sqrt(2))(3 + 2sqrt(2))`
= `(24 + 16sqrt(2) - 15sqrt(2) - 10 xx 2)/(3^2 - (2sqrt(2))^2`
= `(24 + sqrt(2) - 20)/(9 - 8)`
= `4 + sqrt(2)`
= 4 + 1.414
= 5.414
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`5/sqrt 7`
Rationalize the denominator.
`11 / sqrt 3`
Write the lowest rationalising factor of : √24
Write the lowest rationalising factor of : √18 - √50
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : xy
If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m2
Rationalise the denominator `1/sqrt(50)`
Rationalise the denominator `sqrt(75)/sqrt(18)`
Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`
If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`
