Indices and Surds Practice Companion
Now that you've explored why we need numbers like √2 and what the laws of indices are doing, this is where you build fluency with them. Take your time. Get stuck if you need to — getting stuck is part of the work. There are four kinds of help on every question: a Socratic question (which asks you something rather than telling you), a hint (which gives you a piece of the method), a worked solution (which shows the whole thing), and an answer check.
Well done — you've worked through every question. 🌱
Take a moment for the reflection below. You can also press Ctrl+P (or ⌘+P) to print or save your work, including all the reveals and your written workings.
💛 Reflection
Mirroring the Living Body panel of the lesson: how did that feel? There are no wrong answers — these prompts are just to notice what's happening.
- Which question types felt natural? Which felt sticky?
- Were the laws of indices easier or harder than the surd manipulations? What does that tell you about your numerical instincts?
- When you rationalised a denominator with a conjugate, did the trick feel mysterious or sensible? What helped (or what might have helped) it feel sensible?
- On a scale of 1 (no clearer) to 5 (much clearer), how does your understanding of indices and surds feel now compared to before this practice?