Square and cube roots
The power in reverse
What is this about?
The root is the inverse question of the power. The power says: "5² = how much?" (25). The root asks the other way round: "which number squared gives 25?" (5). That's why the best thing you can do to calculate roots is to know your squares well: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...
The rule to remember
√a is the number that multiplied by itself gives a. The cube root ∛a is the number that multiplied by itself THREE times gives a. Trick: always ask yourself "which number squared (or cubed) gives me this?".
Example 1
√49
- 1Ask yourself: which number multiplied by itself gives 49?
- 2Try the squares you know: 6 × 6 = 36, falls short.
- 3Try the next one: 7 × 7 = 49. That's it!
Result: 7
Example 2
∛27
- 1The small 3 means cube root: you're looking for a number that multiplied by itself THREE times gives 27.
- 2Try 2: 2 × 2 × 2 = 8. Too small.
- 3Try 3: 3 × 3 × 3 = 27. Perfect.
Result: 3
The most common mistake
Many people write
√16 = 8
Why it's wrong
16 was divided by 2 instead of looking for the number that squared gives 16. The root is not the half: always check by multiplying. 8 × 8 = 64, which is not 16. But 4 × 4 = 16, so √16 = 4.
Did it click?
The best way to find out is to try. These exercises are exactly on this topic.
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