Structure and calculation Study Guide

To calculate with roots, extract square factors and combine like surds only: for example, √72 = 6√2 and √18 = 3√2, so √72 + √18 = 9√2. For powers with the same non-zero base, add exponents when multiplying, subtract exponents when dividing, and multiply exponents when raising a power to another power. A zero index gives 1, while a negative index represents the reciprocal power.

A systematic listing method organises possibilities in a clear order so that every valid outcome appears once and only once. Choose a consistent feature to vary first, such as the first digit, item or event, then list all matching choices before moving to the next feature. Check the completed list for omissions and repeated outcomes.