Simplify {1}{3-{2}} in the form of p + q√2

Correct Answer is : 373/773 + 27{{2}}{7}72

Correct Answer is : 373/773 + 27{{2}}{7}72

Test Index

JAMB Mathematics 2022 Paper

Question : 7

Total: 39

Simplify

\frac{1}{3-\sqrt{2}}

in the form of p + q√2

Solution:

Concept:

Rationalise the denominator by multiplying by the conjugate of

3-\sqrt{2}

, which is

3+\sqrt{2}

Explanation:

Start with

\frac{1}{3-\sqrt{2}}

Multiply numerator and denominator by

3+\sqrt{2}

\frac{1}{3-\sqrt{2}} \times \frac{3+\sqrt{2}}{3+\sqrt{2}} = \frac{3+\sqrt{2}}{(3-\sqrt{2})(3+\sqrt{2})}

Apply the difference of squares identity:

(3-\sqrt{2})(3+\sqrt{2}) = 3^2 - (\sqrt{2})^2 = 9 - 2 = 7

So the expression simplifies to:

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

Rewrite in the form

p+q\sqrt{2}

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

Answer:

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

, which is option D.

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