Pythagoras: If you have a right angled triangle PQR, and length PQ=5cm, length QR=8cm (which is the longest length), then calculate length PR to two decimal places.

Pythagoras' theorem is: a^2+b^2=c^2 (a=short side, b=short side, c=longest side/hypotenuse, ^=squared). Now applying that to this question would mean that a=PQ, b=PR and c=QR. So we can use the figures given in the question and insert it into the equation as follows: (5^2) + (b^2)=(8^2). Now to calculate the unknown length we need to rearrange the equation which we can do by taking 5^2 to the other side of the equals sign (and when doing so this goes from being positive to negative): b^2 = (8^2)-(5^2). We can simplify this equation by working out what b^2 is equal to: b^2=64-25 and therefore b^2=39. Now to find the answer to what the length PR is we have to square root both sides of the equation and so we get b=√39 and so we can calculate (using a calculator) that b= 6.24499799... and to two decimal places we can say that length PR=6.24cm