Questions: Simplify, be sure to show work to receive credit. Assume all variables represent positive values. Do not use a calculator or round to a decimal. Write the exact simplified form. (2+√28)/6

Solution Steps

To simplify the expression \(\frac{2+\sqrt{28}}{6}\), we first simplify the square root. Since \(\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}\), we can rewrite the expression as \(\frac{2 + 2\sqrt{7}}{6}\). Next, factor out the common factor in the numerator, which is 2, to get \(\frac{2(1 + \sqrt{7})}{6}\). Finally, simplify the fraction by dividing both the numerator and the denominator by 2.

We start with the expression

\[ \frac{2+\sqrt{28}}{6}. \]

First, we simplify \(\sqrt{28}\):

\[ \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}. \]

Substituting back into the expression, we have:

\[ \frac{2 + 2\sqrt{7}}{6}. \]

Next, we factor out the common factor of 2 in the numerator:

\[ \frac{2(1 + \sqrt{7})}{6}. \]

Now, we can simplify the fraction by dividing both the numerator and the denominator by 2:

\[ \frac{1 + \sqrt{7}}{3}. \]

Final Answer