Advertisements
Advertisements
प्रश्न
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
Advertisements
उत्तर
We know that rationalization factor for `7 + 4sqrt3` is `7 - 4sqrt3`. We will multiply numerator and denominator of the given expression `(5 + 2sqrt3)/(7 + 4sqrt3)` by `7 - 4sqrt3` to get
`(5 + 2sqrt3)/(7 + 4sqrt3) xx (7 - 4sqrt3)/(7 - 4sqrt3) = (5xx7 - 5 xx 4sqrt3 + 2 xx 7 xx sqrt3 - 2 xx 4 xx (sqrt3)^2)/((7)^2 - (4sqrt3)^2)`
`= (35 - 20sqrt3 + 14sqrt3 - 8 xx 3)/(49 - 49)`
`= (11 - 6sqrt3)/1`
`= 11 - 6sqrt3`
Hence the given expression is simplified to `11 - 6sqrt3`
APPEARS IN
संबंधित प्रश्न
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
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 \[\frac{1}{x} . \]
\[\sqrt{10} \times \sqrt{15}\] is equal to
The rationalisation factor of \[\sqrt{3}\] is
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
`root(4)root(3)(2^2)` equals to ______.
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
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.
