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In order to remove a surd from the denominator, we must rationalize it by multiplying it by its conjugate. the conjugate of a surd is simply a number that helps formulate the equation:
(a-b)(a+b) = a^2 - b^2
in other terms, the opposite sign of the number.
For this particular equation, our denominator will always be -1. This is because when we multiply a surd with its conjugate, the answer will always be in form of a^2-b^2. When there are too consecutive whole numbers in surd, the denominator will always be -1, when multiplied by its conjugate.
Therefore our denominator is -1. Our numerator is simply : sqrt 1 - sqrt 3…-sqrt 100. Once you start solving this, you will realize that all terms cancel each other out, apart from sqrt1 and sqrt100. This leaves you with :
(sqrt 1 - sqrt 100)/-1
the square root of 1 is always 1 and the square root of 100 is 10. Therefore, our answer will be:
(1-10)/-1
=-9/-1
= 9
Therefore the answer is 9.