Advertisements
Advertisements
Question
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
Advertisements
Solution
`(3 + sqrt(7))/(3 - sqrt(7)`
= `(3 + sqrt(7))/(3 - sqrt(7)) xx (3 + sqrt(7))/(3 + sqrt(7)`
= `(3 + sqrt(7))^2/((3)^2 - (sqrt(7))^2`
= `(9 + 6sqrt(7) + 7)/(9 - 7)`
= `(16 + 6sqrt(7))/(2)`
= `8 + 3sqrt(7)`
= `"a" + "b"sqrt(7)`
Hence, a = 8 and b = 3.
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
If x = `(4 - sqrt(15))`, find the values of
`(1)/x`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x2 + y2
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
Draw a line segment of length `sqrt3` cm.
