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.
problem
Maundy Money
Age
11 to 14
Challenge level
How much money did the Queen give away in pence as a power of 2?
problem
Age of Augustus
Age
11 to 14
Challenge level
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?
problem
The Square of My Age
Age
11 to 14
Challenge level
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?
problem
Square Percentage
Age
11 to 14
Challenge level
What percentage of the integers between 1 and 10,000 are square numbers?
problem
Square Triangle
Age
11 to 14
Challenge level
How many triangles have all three angles perfect squares (in degrees)?
problem
Pythagorean Quadruple
Age
14 to 16
Challenge level
The sum of three square numbers equals $121$. What can those numbers be...
problem
Megabytes and kilobytes
Age
14 to 16
Challenge level
How many bytes are there in one megabyte?
problem
The square and the root
Age
14 to 16
Challenge level
What is the remainder when the square of 49 is divided by the square root of 49?
problem
The power of the sum
Age
14 to 16
Challenge level
What is this sum, expressed as a power of 2?
problem
Powers of Four
Age
14 to 16
Challenge level
Can you work out the value of x in this 'power-full' equation?
problem
Powerful Order
Age
14 to 16
Challenge level
Powers of numbers might look large, but which of these is the largest...
problem
Doubly Powerful
Age
14 to 16
Challenge level
To what power should $4^4$ be raised to give $8^8$?
problem
The power of x
Age
14 to 16
Challenge level
Find the value of $x$ in this equation, where it appears in powers.
problem
How many squares?
Age
14 to 16
Challenge level
How many 4-digit numbers are perfect squares?
problem
root estimation
Age
14 to 16
Challenge level
Which of these is the best approximation for this square root?
problem
Two in a million
Age
14 to 16
Challenge level
What is the highest power of 2 that divides exactly into 1000000?
problem
Powerful expressions
Age
14 to 16
Challenge level
Put these expressions in order, from smallest to largest.
problem
Rough Root
Age
14 to 16
Challenge level
Which of these options is closest to this square root?
problem
Rooted via 10
Age
14 to 16
Challenge level
How many of the numbers shown are greater than 10?
problem
Largest Expression
Age
14 to 16
Challenge level
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?
problem
Roots near 9
Age
14 to 16
Challenge level
For how many integers 𑛠is the difference between √𑛠and 9 is less than 1?
problem
Self-Power Squares
Age
14 to 16
Challenge level
How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?
problem
Power of 3
Age
14 to 16
Challenge level
What power of 27 is needed to get the correct power of 3?
problem
Know Your Powers
Age
14 to 16
Challenge level
Given these equations with unknown powers $x$ and $y$, can you work out $xy$?
problem
power of five
Age
14 to 16
Challenge level
Powers with brackets, addition and multiplication