Advertisements
Advertisements
प्रश्न
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
उत्तर
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
Rationalise the denominators:
⇒ `((7sqrt(3))/(sqrt(10) + sqrt(3)) xx (sqrt(10) - sqrt(3))/(sqrt(10) - sqrt(3))) - ((2sqrt(5))/(sqrt(6) + sqrt(3)) xx (sqrt(6) - sqrt(5))/(sqrt(6) - sqrt(5))) - ((3sqrt(2))/(sqrt(15) + 3sqrt(2)) xx (sqrt(15) - 3sqrt(2))/(sqrt(15) - 3sqrt(2)))`
⇒ `(7sqrt(3)(sqrt(10) - sqrt(3)))/(10 - 3) - (2sqrt(5)(sqrt(6) - sqrt(5)))/(6 - 5) - (3sqrt(2)(sqrt(15) - 3sqrt(2)))/(15 - 8)` ...[∵ a2 – b2 = (a + b)(a – b)]
⇒ `(7sqrt(3)(sqrt(10) - sqrt(3)))/(7) - (2sqrt(5)(sqrt(6) - sqrt(5)))/(1) - (3sqrt(2)(sqrt(15) - 3sqrt(2)))/(3)`
⇒ `(7sqrt(30) - 21)/7 - (2sqrt(30) - 10)/1 + (3sqrt(30) - 18)/3`
⇒ `(21sqrt(30) - 63 - 42sqrt(30) + 210 + 21sqrt(30) - 126)/21`
⇒ `21/21 = 1`
Hence the answer is 1.
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Simplify the following expressions:
`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`
Rationalise the denominator of the following
`(3sqrt2)/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`
`(sqrt5 + 1)/sqrt2`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
if `x = 2 + sqrt3`,find the value of `x^2 + 1/x^2`
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Classify the following number as rational or irrational:
`1/sqrt2`
Value of (256)0.16 × (256)0.09 is ______.
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
