Powers and roots

There are 62 NRICH Mathematical resources connected to Powers and roots
Placeholder: several colourful numbers
problem

Roots near 9

Age
14 to 16
Challenge level
filled star filled star empty star
For how many integers 𝑛 is the difference between √𝑛 and 9 is less than 1?
Double Trouble
problem
Favourite

Double Trouble

Age
14 to 16
Challenge level
filled star empty star empty star
Simple additions can lead to intriguing results...
Function Pyramids
problem

Function Pyramids

Age
16 to 18
Challenge level
filled star empty star empty star

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

Googol
problem

Googol

Age
16 to 18
Challenge level
filled star filled star empty star
Find the smallest value for which a particular sequence is greater than a googol.
Irrational arithmagons
problem

Irrational arithmagons

Age
16 to 18
Challenge level
filled star filled star empty star
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
Fit for photocopying
problem
Favourite

Fit for photocopying

Age
14 to 16
Challenge level
filled star filled star filled star
Explore the relationships between different paper sizes.
Archimedes Numerical Roots
problem

Archimedes Numerical Roots

Age
16 to 18
Challenge level
filled star empty star empty star
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Powerful Order
problem

Powerful Order

Age
14 to 16
Challenge level
filled star filled star empty star
Powers of numbers might look large, but which of these is the largest...
Near 10
problem

Near 10

Age
14 to 16
Challenge level
filled star filled star empty star
10 must remain within easy reach...
Age of Augustus
problem

Age of Augustus

Age
11 to 14
Challenge level
filled star filled star empty star
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?