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 $b \neq 1$.

A-Level Edexcel Maths Pure Quadratics: 3. (a) Simplify $$\sqrt{50}

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{3... 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

To simplify the expression, we first break down the square roots:

Calculate $\sqrt{50}$ : $\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$
Calculate $\sqrt{18}$ : $\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}$
Now substitute these values back into the expression: $5\sqrt{2} - 3\sqrt{2} = (5 - 3)\sqrt{2} = 2\sqrt{2}$

Thus, the simplified form is $2\sqrt{2}$ .

Step 2

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

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Answer

Using the result from part (a):

Substitute $\sqrt{50} - \sqrt{18}$ with $2\sqrt{2}$ : $\frac{12\sqrt{3}}{2\sqrt{2}}$
Simplify the fraction: $= \frac{12}{2} \cdot \frac{\sqrt{3}}{\sqrt{2}} = 6 \cdot \frac{\sqrt{3}}{\sqrt{2}}$ $= 6 \cdot \sqrt{\frac{3}{2}}$

Thus, writing in the form $b\sqrt{c}$ , we have: $6\sqrt{\frac{3}{2}}$ or equivalently, with integer values for $b$ and $c$ , we can write: $= 6\sqrt{3}/\sqrt{2}$

Finally, we rationalize the denominator, multiplying numerator and denominator by $\sqrt{2}$ : $= \frac{6\sqrt{6}}{2} = 3\sqrt{6}$

So the final answer in the required form is $3\sqrt{6}$ .

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

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

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

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

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