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Question
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
Solution
Given that
`(2+sqrt3)(2-sqrt3)`
It can be simplified as
`(2+sqrt3)(2-sqrt3) = 2 xx2-2xxsqrt3+2xx sqrt3 - (sqrt3)^2`
` = 4-2sqrt3+2sqrt3 - `
`= 4-3`
` = 1`
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RELATED QUESTIONS
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
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`
`(2 + sqrt3)/3`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
The rationalisation factor of \[\sqrt{3}\] is
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`(sqrt(10) - sqrt(5))/2`
Simplify:
`(1/27)^((-2)/3)`
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
