Powers and Roots - Short Problems
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?
Square Triangle
How many triangles have all three angles perfect squares (in degrees)?
Maundy Money
How much money did the Queen give away in pence as a power of 2?
Age of Augustus
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?
Square Percentage
What percentage of the integers between 1 and 10,000 are square numbers?
Powers of Four
Can you work out the value of x in this 'power-full' equation?
The Square and the Root
What is the remainder when the square of 49 is divided by the square root of 49?
Pythagorean Quadruple
The sum of three square numbers equals $121$. What can those numbers be...
Largest Expression
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?
Roots Near 9
For how many integers 𑛠is the difference between √𑛠and 9 is less than 1?
The Power of $x$
Find the value of $x$ in this equation, where it appears in powers.
Two in a Million
What is the highest power of 2 that divides exactly into 1000000?
Powerful Expressions
Put these expressions in order, from smallest to largest.
Root Estimation
Which of these is the best approximation for this square root?
Powerful Order
Powers of numbers might look large, but which of these is the largest...
Doubly Powerful
To what power should $4^4$ be raised to give $8^8$?
Power of 3
What power of 27 is needed to get the correct power of 3?
Know Your Powers
Given these equations with unknown powers $x$ and $y$, can you work out $xy$?
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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Seven Squares - Group-worthy Task
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
