This is part of our collection of Short Problems.
You may also be interested in our longer problems on Powers and Roots.
Printable worksheets containing selections of these problems are available here.
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problem
Age of augustus
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?
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problem
The square of my age
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?
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problem
The square and the root
What is the remainder when the square of 49 is divided by the square root of 49?
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problem
Pythagorean quadruple
The sum of three square numbers equals $121$. What can those numbers be...
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problem
Largest expression
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?
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problem
Roots near 9
For how many integers 𑛠is the difference between √𑛠and 9 is less than 1?
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problem
Self-power squares
How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?
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problem
Know your powers
Given these equations with unknown powers $x$ and $y$, can you work out $xy$?