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Powers and Roots Practice Test 5

Question : 16 of 31

Marks: +1, -0

\sqrt{2+\frac{103}{961}}=1+\frac{x}{31}

then x is:

Solution:

Concept:

Simplify the radical and compare both sides after making denominators equal.

Explanation:

Simplify inside the square root:

2+\frac{103}{961}=\frac{1922+103}{961}=\frac{2025}{961}

Take the square root:

\sqrt{\frac{2025}{961}}=\frac{\sqrt{2025}}{\sqrt{961}}=\frac{45}{31}

Write the right-hand side with denominator

31

1+\frac{x}{31}=\frac{31+x}{31}

Equate both sides:

\frac{45}{31}=\frac{31+x}{31}

Cancel the common denominator:

45=31+x

Solve for

x

x=45-31=14

Answer:

x=14

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