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Powers and Roots Practice Test 5

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Question : 10 of 31

Marks: +1, -0

Given that

\frac{52}{x} = \sqrt{ \frac{169}{289} }

, then x equals:

68
62
58
52

Solution:

Concept:

Simplify the square root, then solve the resulting proportion for

x

.

Explanation:

Given:

\frac{52}{x} = \sqrt{\frac{169}{289}}

.

Since

169 = 13^2

and

289 = 17^2

, we get

\sqrt{\frac{169}{289}} = \frac{13}{17}

.

So,

\frac{52}{x} = \frac{13}{17}

.

Cross-multiplying gives

52 \times 17 = 13x

.

Thus,

x = \frac{52 \times 17}{13}

.

Since

52 \div 13 = 4

, we have

x = 4 \times 17 = 68

.

Answer:

x = 68

, so the correct option is A.

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