The sprint is a survival run. The clock starts at one minute. Each correct answer adds 3 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 3 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.
Select "Review answers" on the result screen to see each root you played, with its value.
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.