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प्रश्न
Rationalise the denominator and simplify `(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`
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उत्तर
`(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2)) = ((5sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2)))/((sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2))`
= `(5(3) - 5sqrt(3) xx sqrt(2) + (sqrt(2)sqrt(3) - (2)))/((sqrt(3))^2 - (sqrt(2))^2`
= `(15 - 5sqrt(6) + sqrt(6) - 2)/(3 - 2)`
= `(13 - 4sqrt(6))/1`
= `13 - 4sqrt(6)`
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संबंधित प्रश्न
Rationalize the denominator.
`11 / sqrt 3`
Write the lowest rationalising factor of 5√2.
Write the lowest rationalising factor of √5 - 3.
Write the lowest rationalising factor of : √13 + 3
Find the values of 'a' and 'b' in each of the following:
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x2
If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find mn
If x = `2sqrt3 + 2sqrt2`, find: `1/x`
Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`
If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x2 - y2.
