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 the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Simplify the following:
`3/sqrt(8) + 1/sqrt(2)`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
