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

1 Answer
Mar 28, 2018

Answer:

#(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.