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JAMB Mathematics 2024 Paper

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Question : 50

Total: 50

(

(\sqrt{a} + \sqrt{8a})^2

\sqrt{2}

, a and b are positive integers. Find the value of a and the value of b.

a = 24, b = 6
a = 6, b = 2
a = 6, b = 24
a = 2, b = 6

Solution:

Concept:

Expand the square of the surd expression, then compare the rational and irrational parts.

Explanation:

Write

\sqrt{8a}

as

\sqrt{8}\sqrt{a} = 2\sqrt{2}\sqrt{a}

.

Expand

(\sqrt{a} + \sqrt{8a})^2

using

(x+y)^2 = x^2 + 2xy + y^2

.

This gives

a + 8a + 2\sqrt{a}\sqrt{8a}

.

Simplify:

a + 8a = 9a

.

Also,

2\sqrt{a}\sqrt{8a} = 2\sqrt{8a^2} = 2a\sqrt{8} = 4a\sqrt{2}

.

So the left side becomes

9a + 4a\sqrt{2}

.

Given

9a + 4a\sqrt{2} = 54 + b\sqrt{2}

, compare coefficients.

For the rational part:

9a = 54

, so

a = 6

.

For the surd part:

4a = b

, so

b = 4 \times 6 = 24

.

Answer:

a = 6

and

b = 24

, which is Option C.

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