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JAMB Mathematics 2011 Paper

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Question : 8

Total: 46

Simplify (

\left(\sqrt{2} + \frac{1}{\sqrt[3]{}}\right)\left(\sqrt{2} - \frac{1}{\sqrt[3]{}}\right)

)

$\frac{7}{3}$
$\frac{5}{3}$
$\frac{5}{2}$
$\frac{3}{2}$

Solution:

Concept:

Use the difference of two squares identity:

(a+b)(a-b)=a^2-b^2

.

Explanation:

Let

a=\sqrt{2}

and

b=\frac{1}{\sqrt{3}}

.

Applying the identity:

\left(\sqrt{2}+\frac{1}{\sqrt{3}}\right)\left(\sqrt{2}-\frac{1}{\sqrt{3}}\right)=(\sqrt{2})^2-\left(\frac{1}{\sqrt{3}}\right)^2

Now simplify each square:

(\sqrt{2})^2=2 \quad \text{and} \quad \left(\frac{1}{\sqrt{3}}\right)^2=\frac{1}{3}

Therefore:

2-\frac13=\frac{6}{3}-\frac{1}{3}=\frac{5}{3}

Answer:

\frac{5}{3}

, which is Option B.

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