Advertisements
Advertisements
प्रश्न
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Advertisements
उत्तर
The given number is `1/(sqrt5 + sqrt2)`
On rationalising the denominator,
⇒ `1/(sqrt5 + sqrt2) = 1/(sqrt5 + sqrt2) xx (sqrt5 - sqrt2)/(sqrt5 - sqrt2)`
We know that (a + b) (a - b) = a2 - b2
⇒ `1/(sqrt5 + sqrt2) = (sqrt5 - sqrt2)/((sqrt5)^2 - (sqrt2)^2)`
⇒ `1/(sqrt5 + sqrt2) = (sqrt5 - sqrt2)/(5 - 2)`
∴ `1/(sqrt5 + sqrt2) = (sqrt5 - sqrt2)/3`
APPEARS IN
संबंधित प्रश्न
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`4/sqrt(3)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`1/(sqrt(3) + sqrt(2))`
Simplify:
`(1/27)^((-2)/3)`
If `x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))` and `y = (sqrt(3) - sqrt(2))/(sqrt(3) + sqrt(2))`, then find the value of x2 + y2.
