## 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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