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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### 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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### 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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### 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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### Pythagorean Quadruple

The sum of three square numbers equals $121$. What can those numbers be...

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### Largest Expression

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

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### Roots near 9

For how many integers ð‘› is the difference between âˆšð‘› and 9 is less than 1?

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### 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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### Know Your Powers

Given these equations with unknown powers $x$ and $y$, can you work out $xy$?