Rationalize the denominator 18/3root2+1​

Question

Rationalize the denominator 18/3root2+1​

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Amity 4 years 2021-08-26T00:48:58+00:00 1 Answers 6 views 0

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  1. King
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    2021-08-26T00:50:54+00:00
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    Answer:

    \dfrac{18(3\sqrt2-1)}{17}

    Step-by-step explanation:

    The given expression is :

    x=\dfrac{18}{3\sqrt2+1}

    We need to rationalize the denominator.

    Multiplying and dividing both sides by 3\sqrt2+1 as follows :

    x=\dfrac{18}{3\sqrt2+1}\times \dfrac{3\sqrt2-1}{3\sqrt2-1}\\\\=\dfrac{18(3\sqrt2-1)}{(3\sqrt2)^2-1}\\\\=\dfrac{18(3\sqrt2-1)}{(18-1}\\\\=\dfrac{18(3\sqrt2-1)}{17}

    So, the answer is \dfrac{18(3\sqrt2-1)}{17}.

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