Powers and Roots - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Powers and Roots.

The Square of My Age

KS 3 Short Challenge Level:

Weekly Problem 34 - 2011
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

Square Triangle

KS 3 Short Challenge Level:

Weekly Problem 42 - 2007
How many triangles have all three angles perfect squares (in degrees)?

Maundy Money

KS 3 Short Challenge Level:

Weekly Problem 22 - 2009
How much money did the Queen give away in pence as a power of 2?

Long List

KS 3 Short Challenge Level:

Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?

Tenth Power

KS 3 Short Challenge Level:

Weekly Problem 48 - 2011
Do these powers look odd...

Age of Augustus

KS 3 Short Challenge Level:

Weekly Problem 47 - 2009
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

Factorised Factorial

KS 3 Short Challenge Level:

Weekly Problem 17 - 2010
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

Powerful Zeros

KS 3 Short Challenge Level:

Weekly Problem 32 - 2006
How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

Mini Cross-number

KS 3 & 4 Short Challenge Level:

Weekly Problem 47 - 2014
Which digit replaces x in this crossnumber?

Powerful Order

KS 3 & 4 Short Challenge Level:

Weekly Problem 6 - 2011
Powers of numbers might look large, but which of these is the largest...

Doubly Powerful

KS 3 & 4 Short Challenge Level:

Weekly Problem 38 - 2016
To power should $4^4$ be raised to give $8^8$?

KS 3 & 4 Short Challenge Level:

Weekly Problem 13 - 2011
The sum of three square numbers equals $121$. What can those numbers be...

Powers of Four

KS 3 & 4 Short Challenge Level:

Weekly Problem 52 - 2007
Can you work out the value of x in this 'power-full' equation?

Powerful Finale

KS 3 & 4 Short Challenge Level:

Weekly Problem 24 - 2017
What is the last digit of $3^{2011}$?

Ordering Fractions

KS 3 & 4 Short Challenge Level:

Weekly Problem 46 - 2014
Which of these powers of fractions has greatest value?

Not a Zero

KS 3 & 4 Short Challenge Level:

Weekly Problem 45 - 2017
What is the last non-zero digit of $2^{57} \times 3^4 \times 5^{53}$?

Rooted Via 10

KS 4 Short Challenge Level:

Weekly Problem 22 - 2013
How many of the numbers shown are greater than 10?

Self-power Squares

KS 4 Short Challenge Level:

Weekly Problem 15 - 2016
How many integers $n$, between $1$ and $100$ inclusive, have the property that $n^n$ is a square number?

Largest Expression

KS 4 Short Challenge Level:

Weekly Problem 36 - 2006
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

Powered Up

KS 4 Short Challenge Level:

Weekly Problem 38 - 2014
Can you work out the product of these indices?