Powers and roots

There are 62 NRICH Mathematical resources connected to Powers and roots
Perfectly Square
problem
Favourite

Perfectly square

Age
14 to 16
Challenge level
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The sums of the squares of three related numbers is also a perfect square - can you explain why?
Power mad!
problem
Favourite

Power mad!

Age
11 to 14
Challenge level
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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Pocket money
problem
Favourite

Pocket money

Age
11 to 14
Challenge level
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Which of these pocket money systems would you rather have?
Placeholder: several colourful numbers
problem

Roots near 9

Age
14 to 16
Challenge level
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For how many integers 𝑛 is the difference between √𝑛 and 9 is less than 1?
Function Pyramids
problem

Function pyramids

Age
16 to 18
Challenge level
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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
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Find the smallest value for which a particular sequence is greater than a googol.
Absurdity Again
problem

Absurdity again

Age
16 to 18
Challenge level
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What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
Power Crazy
problem

Power crazy

Age
11 to 14
Challenge level
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What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
Lost in Space
problem

Lost in space

Age
14 to 16
Challenge level
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How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?
Archimedes and numerical roots
problem

Archimedes and numerical roots

Age
14 to 16
Challenge level
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The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?