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Powers and Roots Practice Test 3

Question : 12 of 40

Marks: +1, -0

\sqrt{1 + \frac{x}{144}} = \frac{13}{12}

, what will be the value of x?

Solution:

Concept:

To solve a square-root equation, square both sides and simplify the resulting fraction.

Explanation:

Given:

\sqrt{1+\frac{x}{144}}=\frac{13}{12}

Squaring both sides gives

1+\frac{x}{144}=\left(\frac{13}{12}\right)^2

Now

\left(\frac{13}{12}\right)^2=\frac{169}{144}

So,

1+\frac{x}{144}=\frac{169}{144}

Write

1

\frac{144}{144}

Then

\frac{144+x}{144}=\frac{169}{144}

Cancel the common denominator

144

This gives

144+x=169

Therefore,

x=169-144=25

Check:

\sqrt{1+\frac{25}{144}}=\sqrt{\frac{169}{144}}=\frac{13}{12}

Answer:

x=25

, so the correct option is A.

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