If \;{{2}\;+\;{3}}{{3}} is simplified as m + n{6}, find the value of (m + n)

Correct Answer is : 1 13\;1/331

Correct Answer is : 1 13\;1/331

Test Index

WAEC Mathematics 2015 Paper

Question : 29

Total: 45

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

\sqrt{6}

, find the value of (m + n)

Solution:

Concept:

Rationalise the denominator to express the given surd in the form

m+n\sqrt{6}

, then add the two constants

m

and

n

Explanation:

Start with the given expression:

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

Multiply the numerator and denominator by

\sqrt{3}

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

Simplify the numerator:

\frac{\sqrt{2}\sqrt{3}+\sqrt{3}\sqrt{3}}{(\sqrt{3})^2}

Since

\sqrt{2}\sqrt{3}=\sqrt{6}

and

\sqrt{3}\sqrt{3}=3

, we get:

\frac{\sqrt{6}+3}{3}

Separate the terms:

\frac{3}{3}+\frac{\sqrt{6}}{3}=1+\frac{1}{3}\sqrt{6}

Comparing with

m+n\sqrt{6}

, we have

m=1

and

n=\frac{1}{3}

Therefore:

m+n=1+\frac{1}{3}=1\frac{1}{3}

Answer:

1\frac{1}{3}

Option C.

Go to Question:

Prev Question

Next Question