#1.4A
identify square numbers and cube numbers
#1.4B
calculate squares, square roots, cubes and cube roots
#1.4C
use index notation and index laws for multiplication and division of positive and negative integer powers including zero
#1.4D
express integers as a product of powers of prime factors
\(720 = 2^4 × 3^2 × 5\)
#1.4E
find highest common factors (HCF) and lowest common multiples (LCM)
#1.4F
understand the meaning of surds
Simplify: \(\sqrt{8} + 3\sqrt{32}\)
#1.4G
manipulate surds, including rationalising a denominator
Express in the form \(a + b\sqrt{2}\): \((3 + 5\sqrt{2})^2\)
Rationalise: \(\dfrac{2}{\sqrt{8}}; \quad \dfrac{1}{2-\sqrt{3}}\)
#1.4H
use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers
Evaluate: \(\sqrt[3]{8^2}, \quad 625^{-\frac{1}{2}}, \quad \Big(\dfrac{1}{25}\Big)^{\frac{3}{2}}\)