Advertisements
Advertisements
प्रश्न
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
उत्तर
Let `E = (4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
= `(4sqrt(3) + 5sqrt(2))/(sqrt(16 xx 3) + sqrt(9 xx 2))`
= `(4sqrt(3) + 5sqrt(2))/(4sqrt(3) + 3sqrt(2))`
For rationalising the denominator, multiplying numerator and denominator by `4sqrt(3) - 3sqrt(2)`,
= `(4sqrt(3) + 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) xx ((4sqrt(3) - 3sqrt(2)))/((4sqrt(3) - 3sqrt(2))`
= `(4sqrt(3)(4sqrt(3) - 3sqrt(2)) + 5sqrt(2) (4sqrt(3) - 3sqrt(2)))/((4sqrt(3))^2 - (3sqrt(2))^2` ...[Using identity, (a + b)(a – b) = a2 – b2]
= `(48 - 12sqrt(6) + 20sqrt(6) - 30)/30`
= `(18 + 8sqrt(6))/30`
= `(9 + 4sqrt(6))/15`
APPEARS IN
संबंधित प्रश्न
Rationalise the denominator of the following:
`1/sqrt7`
Simplify the following expressions:
`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Classify the following number as rational or irrational:
`(3+sqrt23)-sqrt23`
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Simplify:
`(1/27)^((-2)/3)`
