identify square numbers and cube numbers

calculate squares, square roots, cubes and cube roots

use index notation and index laws for multiplication and division of positive and negative integer powers including zero

express integers as a product of powers of prime factors

\(720 = 2^4 × 3^2 × 5\)

find highest common factors (HCF) and lowest common multiples (LCM)

understand the meaning of surds

Simplify: \(\sqrt{8} + 3\sqrt{32}\)

manipulate surds, including rationalising a denominator

Express in the form \(a + b\sqrt{2}\): \((3 + 5\sqrt{2})^2\)

Rationalise: \(\dfrac{2}{\sqrt{8}}; \quad \dfrac{1}{2-\sqrt{3}}\)

use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

Evaluate: \(\sqrt[3]{8^2}, \quad 625^{-\frac{1}{2}}, \quad \Big(\dfrac{1}{25}\Big)^{\frac{3}{2}}\)