To add these radicals together their radicands must be the same:

7\( \sqrt{8} \) + 6\( \sqrt{2} \)
7\( \sqrt{4 \times 2} \) + 6\( \sqrt{2} \)
7\( \sqrt{2^2 \times 2} \) + 6\( \sqrt{2} \)
(7)(2)\( \sqrt{2} \) + 6\( \sqrt{2} \)
14\( \sqrt{2} \) + 6\( \sqrt{2} \)

Now that the radicands are identical, you can add them together:

Monica scored 89% on the test meaning she earned 89% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.89 = 213 points. Each question is worth 3 points so she got \( \frac{213}{3} \) = 71 questions right.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (3 + 3) ÷ 2 x 3 - 2²
P: 4 + (6) ÷ 2 x 3 - 2²
E: 4 + 6 ÷ 2 x 3 - 4
MD: 4 + \( \frac{6}{2} \) x 3 - 4
MD: 4 + \( \frac{18}{2} \) - 4
AS: \( \frac{8}{2} \) + \( \frac{18}{2} \) - 4
AS: \( \frac{26}{2} \) - 4
AS: \( \frac{26 - 8}{2} \)
\( \frac{18}{2} \)
9

If 75% of the town's 19,000 voters cast ballots the number of votes cast is:

(\( \frac{75}{100} \)) x 19,000 = \( \frac{1,425,000}{100} \) = 14,250

The mayor got 63% of the votes cast which is:

(\( \frac{63}{100} \)) x 14,250 = \( \frac{897,750}{100} \) = 8,978 votes.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{4}} \)
\( \frac{\sqrt{9}}{\sqrt{4}} \)
\( \frac{\sqrt{3^2}}{\sqrt{2^2}} \)
\( \frac{3}{2} \)
1\(\frac{1}{2}\)