Number Structured Questions | Cambridge O Level Mathematics (Syllabus D)

Question 1 of 7 · 8 marks

Number · 1 - Primes, Roots & Surds

4 parts

Mathematics (Syllabus D) 4024 · Question 1Paper 2 · Calculator[8 marks]

(a)

Express $504$ as a product of its prime factors in index form.

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(b)

The integer $504k$ is a perfect square, where $k$ is a positive integer. Find the smallest possible value of $k$ .

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(c)

Simplify completely $\frac{\sqrt{504}}{\sqrt{14}}$ , giving your answer as an integer.

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(d)

Express $\frac{6}{\sqrt{7} - 1}$ in the form $a + \sqrt{b}$ , where $a$ and $b$ are integers.

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