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Powers and Roots Practice Test 2

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Question : 11 of 40

Marks: +1, -0

If

\sqrt{5} = 2.236

, then find the value of

\frac{\sqrt{5}}{2} - \frac{10}{\sqrt{5}} + \sqrt{125}

.

10.062
8.944
7.826
5.59

Solution:

Concept:

Simplify all radical terms in terms of

\sqrt{5}

, then substitute the given value.

Explanation:

Given

\sqrt{5}=2.236

.

Rationalize

\frac{10}{\sqrt{5}}

:

\frac{10}{\sqrt{5}} = \frac{10}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = 2\sqrt{5}

.

Also,

\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}

.

So the expression becomes:

\frac{\sqrt{5}}{2} - 2\sqrt{5} + 5\sqrt{5}

= \left(\frac{1}{2} - 2 + 5\right)\sqrt{5}

= \frac{7}{2}\sqrt{5}

Substitute

\sqrt{5}=2.236

:

\frac{7}{2} \times 2.236 = 7.826

.

Answer:

7.826

(Option C)

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