Advertisements
Advertisements
प्रश्न
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
उत्तर
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
Rationalizing the denominator of each term, we have
= `(4sqrt(3)(2 + sqrt(2)))/((2 - sqrt(2))(2 + sqrt(2))) - (30(4sqrt(3) + 3sqrt(2)))/((4sqrt(3) - 3sqrt(2))(4sqrt(3) + 3sqrt(2))) - (3sqrt(2)(3 - 2sqrt(3)))/((3 + 2sqrt(3))(3 - 2sqrt(3))`
= `(8sqrt(3) + 4sqrt(6))/(4 - 2) - (120sqrt(3) + 90sqrt(2))/(48 - 18) - (9sqrt(2) - 6sqrt(6))/(9 - 12)`
= `(8sqrt(3) + 4sqrt(6))/(2) - (120sqrt(3) + 90sqrt(2))/(30) - (9sqrt(2) - 6sqrt(6))/(-3)`
= `(8sqrt(3) + 4sqrt(6))/(2) - (120sqrt(3) + 90sqrt(2))/(30) - (9sqrt(2) - 6sqrt(6))/(3)`
= `4sqrt(3) + 2sqrt(6) - 4sqrt(3) - 3sqrt(2) + 3sqrt(2) - 2sqrt(6)`
= 0
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/(sqrt 3 - sqrt 2)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Draw a line segment of length `sqrt5` cm.
