Advertisements
Advertisements
प्रश्न
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
Advertisements
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
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Write the reciprocal of \[5 + \sqrt{2}\].
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
The rationalisation factor of \[\sqrt{3}\] is
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
`1/(sqrt(9) - sqrt(8))` is equal to ______.
Value of (256)0.16 × (256)0.09 is ______.
