# Exam-Style Questions on Surds

## Problems on Surds adapted from questions set in previous Mathematics exams.

### 1.

GCSE Higher

(a) Without using a calculator, show that $$\sqrt{28}=2\sqrt7$$

The point $$X$$ is shown on the unit grid below. The point $$Y$$ is $$\sqrt17$$ units from $$X$$ and lies on the intersection of two grid lines. Mark one possible position for $$Y$$.

### 2.

GCSE Higher

(a) Express $$\sqrt{5} + \sqrt{20}$$ in the form $$a \sqrt{5}$$ where $$a$$ is an integer.

(a) Express $$( \frac{1}{ \sqrt{5} } ) ^ 9$$ in the form $$\frac{ \sqrt{b}}{c}$$ where $$b$$ and $$c$$ are integers.

### 3.

GCSE Higher

(a) Write this list of numbers in order, smallest first.

$$\sqrt{47}, \frac{22}{3}, 3.5^2, 8.64$$

(b) Write $$(1 + \sqrt5)^2$$ in the form $$a + b\sqrt5$$ .

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