Advertisements
Advertisements
प्रश्न
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
Advertisements
उत्तर
We have, `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`
= `(4(3sqrt(3) + 2sqrt(2)) + 3(3sqrt(3) - 2sqrt(2)))/((3sqrt(3) - 2sqrt(2))(3sqrt(3) + 2sqrt(2))`
= `(12sqrt(3) + 8sqrt(2) + 9sqrt(3) - 6sqrt(2))/((3sqrt(3))^2 - (2sqrt(2))^2` ...[Using identity, (a + b)(a – b) = a2 – b2]
= `(21sqrt(3) + 2sqrt(2))/(27 - 8)`
= `(21sqrt(3) + 2sqrt(2))/19`
= `(21 xx 1.732 + 2 xx 1.414)/19` ...`["Put" sqrt(2) = 1.414 "and" sqrt(3) = 1.732]`
= `(36.372 + 2.828)/19`
= `39.2/19`
= 2.06316
= 2.063
APPEARS IN
संबंधित प्रश्न
Represent `sqrt9.3` on the number line.
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
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`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
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`
`(3 - sqrt5)/(3 + 2sqrt5)`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
\[\sqrt{10} \times \sqrt{15}\] is equal to
`1/(sqrt(9) - sqrt(8))` is equal to ______.
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
