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Simplify the following expressions:

`(11 + sqrt11)(11 - sqrt11)`

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#### Solution

We know that `(a + b)(a - b) = a^2 - b^2` We will use this property to simplify the expression

`(11 + sqrt11)(11 - sqrt11)`

`∴ (11 + sqrt11)(11 - sqrt11) = 11^2 - (sqrt11)^2`

`= 11 xx 11 - sqrt11 xx sqrt11`

`= 121 - sqrt(11 xx 11)`

`= 121 - (11^2)^(1/2)`

= 121 - 11

= 110

Hence the value of expression is 110.

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