How do you simplify 5/(8+square root of 7)?

1 Answer
Jacob S.
Mar 28, 2018

(40-5sqrt7)/57

Explanation:

Since the equation 5/(8+sqrt7) has a radical in the denominator, it must be rationalized. However, you cannot simply multiply the numerator and denominator by sqrt7, because the denominator would still remain as 8sqrt7 + 7.

Instead, you must multiply by the conjugate of 8+sqrt7, which is 8-sqrt7. The conjugate of something is simply swapping the sign of the equation from either negative to positive, or vise versa.

Multiplying by the conjugate,

5/(8+sqrt7) * (8-sqrt7)/(8-sqrt7)

Since the denominator consists of two binomials, you must FOIL it. The 5 on the numerator can simply be distributed. If you are unsure as to what FOILing is, reference this: https://en.wikipedia.org/wiki/FOIL_method

After the previous step, you are left with:

(40-5sqrt7)/57

Which cannot be simplified any further.

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