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
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
The rationalisation factor of \[\sqrt{3}\] is
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
