Nat 5 Maths — Surds Session 1

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Welcome to Surds

Session 1 · Simplifying surds · Nat 5 Maths

Work out each answer in your jotter, then type it in.
Use the √ toolbar to enter surd notation.

A surd is an irrational square root — one that cannot be simplified to a whole number or a terminating decimal.

For example:

√(a × b) = √a × √b

We use this to split a number under a root sign into a perfect square multiplied by something else.

Example — Simplify √12

√12 = √(4 × 3) = √4 × √3 = 2√3

Example — Simplify √45

√45 = √(9 × 5) = √9 × √5 = 3√5

Example — Simplify √50

√50 = √(25 × 2) = √25 × √2 = 5√2

Find the largest perfect square that divides into your number (4, 9, 16, 25, 36, 49…)
Rewrite the number under the root as perfect square × other factor
Split using √(a × b) = √a × √b
Take the square root of the perfect square — write it out front
Check: can the surd part simplify further? If so, repeat!

Section A — Practice Questions

Section B — Stretch Questions

Challenge: These questions need a bit more thought — some involve choosing the best perfect square factor, others have two-step simplification.

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