2007 CEMC Pascal Problems/Problem 6

Problem

The value of $\frac{\sqrt{64} + \sqrt{36}}{\sqrt{64 + 36}}$ is

$\text{ (A) }\ \frac{7}{5} \qquad\text{ (B) }\ \frac{16}{5} \qquad\text{ (C) }\ \frac{1}{5} \qquad\text{ (D) }\ \frac{24}{5} \qquad\text{ (E) }\ \frac{14}{5}$

Solution 1

We get $\frac{\sqrt{64} + \sqrt{36}}{\sqrt{64 + 36}} = \frac{8 + 6}{\sqrt{100}} = \frac{14}{10}$

Simplifying, we have $\frac{14 \div 2}{10 \div 2} = \boxed {\textbf {(A) } \frac{7}{5}}$

~anabel.disher

Solution 1.5

We can remember that $6^2 + 8^2 = 10^2$ using pythagorean triples. $6^2 = 36$ and $8^2 = 64$ , so we have:

$\frac{8 + 6}{10}$

Using the same process as solution 1, we get $\boxed {\textbf {(A) } \frac{7}{5}}$ .

~anabel.disher

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2007 CEMC Pascal Problems/Problem 6

Problem

Solution 1

Solution 1.5