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प्रश्न
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
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उत्तर
`[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ] xx [ 2√5 + 3√2 ]/[ 2√5 + 3√2 ]`
= `[( 2sqrt5 + 3sqrt2)^2]/[ (2sqrt5)^2 - (3sqrt2)^2]`
= `[ 4 xx 5 + 9 xx 2 + 12sqrt10 ]/[ 20 -18 ]`
= `[ 20 + 18 + 12sqrt10 ]/2`
= `[ 38 + 12sqrt10 ]/2`
= `[2( 19 + 6sqrt10 )]/2`
= 19 + 6√10
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संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
