Answer:
10 + 3(√6)
Step-by-step explanation:
To simplify this expression, take what is divisible by 2 in the numerator (top) out of the fraction. For the square root number, change it to a mixed radical form (an equivalent number multiplied by a smaller root) by taking out square numbers.
[tex]\frac{20+\sqrt{216}}{2}[/tex] Split the fraction to see what can be divided
[tex]=\frac{20}{2}+\frac{\sqrt{216}}{2}[/tex] 20/2 = 10
[tex]=10+\frac{\sqrt{216}}{2}[/tex] Simplify the root. 216 = 4*9*6
[tex]=10+\frac{\sqrt{4*9*6}}{2}[/tex] 4 and 9 are square numbers. Take out the square root of those factors.
[tex]=10+\frac{2\sqrt{9*6}}{2}[/tex] Took out the √4 first.
[tex]=10+\frac{2*3\sqrt{6}}{2}[/tex] Took out √9. (√4)(√9) = 2*3
[tex]=10+\frac{6\sqrt{6}}{2}[/tex] The mixed radical is 6√6. Divide it by 2.
[tex]=10+3\sqrt{6}[/tex] Answer
