Powers and Roots - Short Problems

A collection of short Stage 3 and 4 problems on powers and roots.



Weekly Problem 48 - 2011

Challenge Level: Challenge Level:1

Do these powers look odd...

Weekly Problem 51 - 2011

Challenge Level: Challenge Level:1

The equation $x^2+2=y^3$ looks nearly quadratic. What integer solutions can you find?

Weekly Problem 6 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

From this sum of powers, can you find the sum of the indices?

Weekly Problem 22 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

How much money did the Queen give away in pence as a power of 2?

Weekly Problem 47 - 2009

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 17 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 33 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

Weekly Problem 6 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Powers of numbers might look large, but which of these is the largest...

Weekly Problem 13 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 34 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 38 - 2014

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 38 - 2014

Weekly Problem 46 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 46 - 2014

Weekly Problem 47 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 47 - 2014