3. (a) Simplify $$\sqrt{50} - \sqrt{18}$$ giving your answer in the form $a\sqrt{2}$, where $a$ is an integer. (b) Hence, or otherwise, simplify $$\frac{12\sqrt{3}}{\sqrt{50} - \sqrt{18}}$$ giving your answer in the form $b\sqrt{c}$, where $b$ and $c$ are integers and $b \neq 1$.

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3. (a) Simplify $$\sqrt{50} - \sqrt{18}$$ giving your answer in the form $a\sqrt{2}$, where $a$ is an integer - Edexcel - A-Level Maths Pure - Question 5 - 2016 - Paper 1

Question 5

$3.-(a)-Simplify--$$\sqrt{50}---\sqrt{18}$$--giving-your-answer-in-the-form-$a\sqrt{2}$,-where-$a$-is-an-integer-Edexcel-A-Level Maths Pure-Question 5-2016-Paper 1.png$

3. (a) Simplify $$\sqrt{50} - \sqrt{18}$$ giving your answer in the form $a\sqrt{2}$, where $a$ is an integer. (b) Hence, or otherwise, simplify $$\frac{12\sqrt{... show full transcript

Worked Solution & Example Answer:3. (a) Simplify $$\sqrt{50} - \sqrt{18}$$ giving your answer in the form $a\sqrt{2}$, where $a$ is an integer - Edexcel - A-Level Maths Pure - Question 5 - 2016 - Paper 1

Step 1

Simplify $$\sqrt{50} - \sqrt{18}$$

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Answer

$\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$ and $\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}$ . Therefore, we have:

$\sqrt{50} - \sqrt{18} = 5\sqrt{2} - 3\sqrt{2} = 2\sqrt{2}$ .

So, the answer is $2\sqrt{2}$ , where $a = 2$ .

Step 2

Hence, or otherwise, simplify $$\frac{12\sqrt{3}}{\sqrt{50} - \sqrt{18}}$$

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Answer

We know from part (a) that $\sqrt{50} - \sqrt{18} = 2\sqrt{2}$ . Therefore, substituting this into our expression:

$\frac{12\sqrt{3}}{2\sqrt{2}} = \frac{12}{2} \cdot \frac{\sqrt{3}}{\sqrt{2}} = 6\cdot \frac{\sqrt{3}}{\sqrt{2}} = 6\cdot \sqrt{\frac{3}{2}} = 6\cdot \frac{\sqrt{6}}{2} = 3\sqrt{6}$ .

Thus, the answer is $3\sqrt{6}$ , where $b = 3$ and $c = 6$ .

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