Squares and roots
Recall square numbers, cube numbers and the roots that undo them. Twelve typed items a round.
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Example
Example
25² = [ ]
A number ending in 5: 2 × 3 = 6, then write 25 after it. The answer is 625.
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No clock. The method is shown after each answer.
Squares of 2 to 15, and the roots of those squares.
12 items · No time limit
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Squares and roots
Pick a level and a round, then press Start.
Explore the method
Square a number by working from the round number next to it, and estimate a root from the two nearest squares.
On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is usedHelp
Read the item and type the answer. Press Enter to check it. In an untimed round, press Enter again for the next item.
A square is a number times itself, so 17² is 17 × 17, which is 289. A square root undoes that, so the square root of 289 is 17. A cube is the number times itself twice more, so 7³ is 343.
Levels 1 to 3 use perfect squares. Level 1 uses squares of 2 to 15 and the roots of those squares. Level 2 goes up to 25. Level 3 combines squares near round tens or ending in 5 up to 75, roots of squares up to 30², cubes up to 10 and their cube roots. Level 4 asks you to estimate the square root of a number that is not a square.
On level 4 an answer within 0.1 of the true root counts as correct. The number is between 17 and 899. The review shows the two nearest squares and how to read between them.
An untimed round shows the method after each answer. A 2-minute sprint gives you two minutes for all twelve items, moves straight to the next item, and keeps the methods for the end. The sprint is on levels 1 to 3.
Your score is how many of the twelve you answered correctly. It is arithmetic practice, not a measure of ability. Finish the round to save it in this browser. A sprint whose clock runs out is saved too, and the items you did not reach count as wrong. Ending early with Escape or End saves nothing.
Type digits, and one decimal place on level 4. Enter checks your answer. In an untimed round Enter again moves to the next item. Escape ends the round. End ends it too, except while the caret is in the answer box.
About this practice
Learn a method
Squares near round numbersRecall square numbers, cube numbers and the roots that undo them. Twelve typed items a round.
Report a problem
On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is used