Rationalize the denominator of the fraction: √5/√8 – √3

Question

Rationalize the denominator of the fraction: √5/√8 – √3

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Thanh Thu 1 year 2021-09-02T01:59:31+00:00 1 Answers 10 views 0

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    2021-09-02T02:00:37+00:00

    Answer:

    Step-by-step explanation:

    Remark

    The editor must have brackets put around the denominator when there are 2 terms.

    That means I think the question is (√5) / (√8 – √3). If this is incorrect, leave a note.

    To rationalize the denominator, you must multiply numerator and denominator by the conjugate  (√8 + √3).

    Solution

    √5 *  (√8 – √3) /  ( (√8 – √3) *  (√8 + √3)  )  

    I don’t think there is any point in removing the brackets in the numerator. Just leave it.

    The denominator is a different matter.

    denominator = ( (√8 – √3) *  (√8 + √3)  )

    √8 * √8 = 8

    √8 * √3 = √24

    – √3 * √8 = – √24

    -√3 * √3 = – 3

    Take a close look at the 2 middle terms. They cancel out because one of them is plus and the other minus.

    What you are left with is 8 – 3 = 5

    So the final answer is

    √5 *  (√8 – √3)

    =============

    5

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