Square and Cube Root Laws

Mathematics — Second Preparatory

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Find the value of √49 + ³√(−27).	Findvalue
Solution	√49 = 7, and ³√(−27) = −3, because (−3)³ = −27. So the sum is 7 + (−3) = 4.	because
Example 2	Find √((−5)²) then find √(4x²) when x = −3	Findthen
Solution	√((−5)²) = \|−5\| = 5. When x = −3 4x² = 4 × 9 = 36 so √36 = 6
Example 3	Simplify √72	Simplify
Solution	The largest perfect square that divides 72 is 36. So √72 = √36 × √2 = 6√2	largestperfectsquaredivides
Example 4	Find the value of ³√(8 ÷ 27).	Findvalue
Solution	Split the root over the numerator and the denominator: ³√8 ÷ ³√27 = 2 ÷ 3 = 2/3. Check: (2/3)³ = 8/27.	Splitrootovernumerator

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