Advertisements
Advertisements
प्रश्न
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
उत्तर
`1/(sqrta + sqrtb) xx ((sqrta - sqrtb)/(sqrta - sqrtb)) = (sqrta - sqrtb)/(a - b)`
`{1/(sqrta + sqrtb) = (sqrta - sqrtb)/(a - b)}`
= `2/1 ((sqrt5 - sqrt3)/(5 - 3)) + ((sqrt3 - sqrt2)/(3-2)) - (3/1)((sqrt5 - sqrt2)/(5 - 2))`
= `cancel2 xx (sqrt5 - sqrt3)/cancel2 + (sqrt3 - sqrt2)/1 = cancel3 xx (sqrt5 - sqrt2)/cancel3`
= `cancelsqrt5 - cancelsqrt3 + cancelsqrt3 - cancelsqrt2 - cancelsqrt5 + cancelsqrt2`
= 0
APPEARS IN
संबंधित प्रश्न
Simplify of the following:
`root(4)1250/root(4)2`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`3/sqrt10`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of x and y.
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
