Martin did this question. Rationalise the denominator of $$\frac{14}{2 + \sqrt{3}}$$ Here is how he answered the question. $$\frac{14}{2 + \sqrt{3}} = \frac{14 \times (2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})}$$ $$= \frac{28 - 14\sqrt{3}}{4 - 3}$$ $$= \frac{28 - 14\sqrt{3}}{1}$$ $$= 28 - 14\sqrt{3}$$ Martin's answer is wrong. (a) Find Martin's mistake. Sian did this question. Rationalise the denominator of $$\frac{5}{\sqrt{12}}$$ Here is how she answered the question. $$\frac{5}{\sqrt{12}} = \frac{5 \times \sqrt{12}}{\sqrt{12} \times \sqrt{12}}$$ $$= \frac{5 \times 2\sqrt{3}}{12}$$ $$= \frac{5\sqrt{3}}{4}$$ Sian's answer is wrong. (b) Find Sian's mistake.

GCSE Edexcel Maths Rounding, Estimation & Bounds: Martin did this question. Ratio

Martin did this question - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

Question 21

Martin did this question. Rationalise the denominator of $$\frac{14}{2 + \sqrt{3}}$$ Here is how he answered the question. $$\frac{14}{2 + \sqrt{3}} = \frac{14 \... show full transcript

Worked Solution & Example Answer:Martin did this question - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

Step 1

Find Martin's mistake.

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Answer

Martin made an error while rationalizing the denominator. He should have multiplied the numerator and denominator by the conjugate of the denominator correctly.

The correct approach is:

$\frac{14}{2 + \sqrt{3}} \times \frac{2 - \sqrt{3}}{2 - \sqrt{3}} = \frac{14(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})}$

This gives:

$= \frac{28 - 14\sqrt{3}}{4 - 3} = \frac{28 - 14\sqrt{3}}{1} = 28 - 14\sqrt{3}$

Finally, we should verify that this answer is correct when simplifying the expression. The mistake was assuming the denominator simplified directly to 1 without calculating it.

Step 2

Find Sian's mistake.

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Answer

Sian's mistake occurred in the application of the properties of square roots. She incorrectly used the formula for multiplying the square roots of the denominator.

The proper method to rationalize the denominator should have been:

$\frac{5}{\sqrt{12}} \times \frac{\sqrt{12}}{\sqrt{12}} = \frac{5 \times \sqrt{12}}{12} = \frac{5 \sqrt{12}}{12}$

Then, reducing further using $\sqrt{12} = 2\sqrt{3}$ results in:

$\frac{5 \times 2\sqrt{3}}{12} = \frac{10\sqrt{3}}{12} = \frac{5\sqrt{3}}{6}$

Thus, Sian should have simplified her final answer to ( \frac{5\sqrt{3}}{6} ).

Martin did this question - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

Worked Solution & Example Answer:Martin did this question - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

Find Martin's mistake.

Find Sian's mistake.

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