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प्रश्न
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
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उत्तर
The given expression is `(sqrt5 - sqrt2) (sqrt5 + sqrt2)`
We know that (a + b) (a - b) = a2 - b2
⇒ `(sqrt5 - sqrt2) (sqrt5 + sqrt2) = (sqrt5)^2 - (sqrt2)^2`
⇒ `(sqrt5 - sqrt2) (sqrt5 + sqrt2) = 5 - 2`
∴ `(sqrt5 - sqrt2) (sqrt5 + sqrt2) = 3`
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संबंधित प्रश्न
Rationalise the denominator of the following:
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Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
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Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
Write the reciprocal of \[5 + \sqrt{2}\].
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Find the value of a and b in the following:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = a + 7/11 sqrt(5)b`
