Powers and roots

There are 62 NRICH Mathematical resources connected to Powers and roots
Double Trouble
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Double trouble

Age
14 to 16
Challenge level
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Simple additions can lead to intriguing results...
Surds
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Surds

Age
14 to 16
Challenge level
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Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
What an odd fact(or)
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What an odd fact(or)

Age
11 to 14
Challenge level
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Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
Giants
problem
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Giants

Age
16 to 18
Challenge level
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Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
In Between
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In between

Age
16 to 18
Challenge level
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Can you find the solution to this algebraic inequality?
Negative Power
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Negative power

Age
14 to 16
Challenge level
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What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
Guesswork
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Guesswork

Age
14 to 16
Challenge level
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Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Ab Surd Ity
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Ab surd ity

Age
16 to 18
Challenge level
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Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
Perfectly Square
problem
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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
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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.