Simplify 2√7- \;{14}{{7}} + \;{7}{{21}}

Correct Answer is : 213\;{{21}}{3}321

Correct Answer is : 213\;{{21}}{3}321

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WAEC Mathematics 2021 Paper

Question : 12

Total: 49

\;\frac{14}{\sqrt{7}} + \;\frac{7}{\sqrt{21}}

Solution:

Concept:

Rationalise surds with irrational denominators, then combine like terms.

Explanation:

Rationalise the second term:

\frac{14}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{14\sqrt{7}}{7} = 2\sqrt{7}

Rationalise the third term:

\frac{7}{\sqrt{21}} \times \frac{\sqrt{21}}{\sqrt{21}} = \frac{7\sqrt{21}}{21} = \frac{\sqrt{21}}{3}

Substitute these into the original expression:

2\sqrt{7} - 2\sqrt{7} + \frac{\sqrt{21}}{3}

The terms

2\sqrt{7}

and

-2\sqrt{7}

cancel out, leaving

0 + \frac{\sqrt{21}}{3}

Therefore, the simplified form is

\frac{\sqrt{21}}{3}

Answer:

\frac{\sqrt{21}}{3}

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