Operations on Real Numbers

Mathematics — Second Preparatory

Multiplying and dividing roots

√a × √b = √(a × b), for example √2 × √8 = √16 = 4.
√a ÷ √b = √(a ÷ b), for example √50 ÷ √2 = √25 = 5.
To simplify a root, we take out the largest perfect square that divides the number under it. For example, √50 = √25 × √2 = 5√2.
Another example √3 × √12 = √36 = 6. We can check it by simplifying √12 = 2√3, so √3 × 2√3 = 2 × 3 = 6. Similarly, √20 ÷ √5 = √4 = 2.
When several roots appear in an expression, we add or subtract them only after simplifying them.
Check √27 − √12 = 3√3 − 2√3 = √3, because after simplification both roots become like roots.

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