Powers and roots
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Surds
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
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What an odd fact(or)
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
5?
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Giants
Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
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Negative power
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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Guesswork
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.
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Ab surd ity
Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of
cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
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Perfectly square
The sums of the squares of three related numbers is also a perfect square - can you explain why?
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Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.