# 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.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 4 ★★ Sheet 1 Solutions

### Square Triangle

##### KS 3 Short Challenge Level:

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

### Mini Cross-number

##### KS 3 Short Challenge Level:

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

### 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?

### Megabytes and Kilobytes

##### KS 3 Short Challenge Level:

How many bytes are there in one megabyte?

### 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?

### Tenth Power

##### KS 3 Short Challenge Level:

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

### Square Percentage

##### KS 3 Short Challenge Level:

Weekly Problem 36 - 2016
What percentage of the integers between 1 and 10,000 are square numbers?

### 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?

### Powerful Order

##### KS 4 Short Challenge Level:

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

##### KS 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 4 Short Challenge Level:

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

##### KS 4 Short Challenge Level:

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

### 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?

### Huge Powers

##### KS 4 Short Challenge Level:

Can you put these numbers in order?

### Rooted Via 10

##### KS 4 Short Challenge Level:

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

### Doubly Powerful

##### KS 4 Short Challenge Level:

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

### 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?

### Not a Zero

##### KS 4 Short Challenge Level:

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

### Power of 3

##### KS 4 Short Challenge Level:

What power of 27 is needed to get the correct power of 3?

### Powered Up

##### KS 4 Short Challenge Level:

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