The sprint is a survival run. The clock starts at one minute. Each correct answer adds 5 seconds to the clock. The run ends when the clock reaches zero, or when you work out the 30th root.
The quiz shows one root at a time. The roots get harder every 5 answers, in 6 levels. Level 1 is √49. Level 6 is √3969, ∛19683 and ⁵√100000.
How to play
The clock starts at your first keystroke, not when the page opens.
You start with one minute. Each correct answer adds 5 seconds.
Roots come one at a time, in order. You cannot skip one.
Type the value. An exact match commits at once. Enter is optional.
A wrong answer on Enter shakes the box and clears it. There is no penalty, but the clock keeps running.
Every 5 answers, the roots move up one level. There are 6 levels.
The run ends when the clock reaches zero, or when you work out all 30 roots.
Your score is the number of roots you worked out. A full 30 ranks by time: the fastest player is first.
What counts in this quiz
Up to 30 roots per run, in 6 levels of 5. Every root is a perfect power, so every answer is a whole number.
Level 1: square roots to √100. Level 2: square roots to √400 and cube roots to ∛125. Level 3: square roots to √900, cube roots to ∛1000, fourth roots to ∜625.
Level 4: square roots to √1600, cube roots to ∛3375, fourth roots to ∜10000, fifth roots to ⁵√1024. Level 5: square roots to √2500, cube roots to ∛8000, fifth and sixth roots, ⁷√128 and ⁸√256. Level 6: square roots to √4900, cube roots to ∛27000, higher roots to ¹⁰√1024.
The small number before the root sign is the index: ∛ is the cube root, ∜ the fourth root, ⁵√ the fifth root.
What's not included — and why
No root of a number that is not a perfect power. There are no decimal answers.
Good to know
The root sign √ is thought to be a stylised letter r, for radix, the Latin word for root. It first appeared in print in 1525.
√2 was the first number shown to be irrational, about 2,500 years ago. Legend says the Pythagoreans drowned the man who proved it.