Rationalise the denominator and simplify 6/(√(5) - √(2)).

Question 48

MediumOriginal question

Rationalise the denominator and simplify $\frac{6}{\sqrt{5} - \sqrt{2}}$ .

2(\sqrt{5} - \sqrt{2})

Correct answerYour answer

\frac{6(\sqrt{5} + \sqrt{2})}{7}

Correct answerYour answer

\sqrt{5} + \sqrt{2}

Correct answerYour answer

2(\sqrt{5} + \sqrt{2})

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Multiply top and bottom by the conjugate $\sqrt{5} + \sqrt{2}$ .
Denominator: $(\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3$ .
Value $= \frac{6(\sqrt{5} + \sqrt{2})}{3} = 2(\sqrt{5} + \sqrt{2})$ .

Worth noting

The denominator becomes $5 - 2$ , not $5 + 2$ ; using 7 gives $\frac{6(\sqrt{5} + \sqrt{2})}{7}$ . Keeping the minus sign in the answer forgets that the conjugate flips it.

Concept: Rationalising with the conjugate surd
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsPowers, roots and surds

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Ten questions from Simplification & Approximation, at your own pace.

Rationalise the denominator and simplify 65−2\frac{6}{\sqrt{5} - \sqrt{2}}5​−2​6​.

Explanation

Rationalise the denominator and simplify $\frac{6}{\sqrt{5} - \sqrt{2}}$ .