Rationals Between

What fractions can you find between the square roots of 56 and 58?

Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

Consecutive Squares

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Powers of Four

Stage: 3 and 4 Short Challenge Level:

Note that $4^x+4^x+4^x+4^x = 4 \times 4^x$ = $4^{x+1}$ .

So $x+1=16$, hence $x = 15$

This problem is taken from the UKMT Mathematical Challenges.
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