Advertisements
Advertisements
प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Advertisements
उत्तर
`3/(2 sqrt 5 - 3 sqrt 2)`
`= 3/(2 sqrt 5 - 3 sqrt 2) xx (2 sqrt 5 + 3 sqrt 2)/(2 sqrt 5 + 3 sqrt 2)`
`= (3(2 sqrt 5 + 3 sqrt 2))/((2 sqrt 5)^2 - (3 sqrt 2)^2)`
.....`[("a" + "b")("a" - "b") = "a"^2 - "b"^2]`
`= (3(2 sqrt 5 + 3 sqrt 2))/(4 xx 5 - 9 xx 2)`
`= (3(2 sqrt 5 + 3 sqrt 2))/(20 - 18)`
`= (3(2 sqrt 5 + 3 sqrt 2))/2`
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
Rationalize the denominator.
`12/(4sqrt3 - sqrt 2)`
Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
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:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Draw a line segment of length `sqrt5` cm.
