Skip to main content

King's Maths School

Challenge 470: An Absurd Workout

A tricky technical trial that will take tenacity - I promise it simplifies neatly at the end!

Warm-up

Simplify the following expression:

(√2+√3+√5)(√2+√3-√5)(√2-√3+√5)(-√2+√3+√5)

[Your answer should be an integer]

The challenge

Replace each __ in the following expression with + or - so that the expression simplifies to give an integer. You should be able to do it without a calculator!

(√2__√3__√5__√7)(√2__√3__√5__√7)(√2__√3__√5__√7)(√2__√3__√5__√7)(√2__√3__√5__√7)(√2__√3__√5__√7)(√2__√3__√5__√7)(√2__√3__√5__√7)

[If it's too big for your screen, you should see eight of the same bracket multiplied together]

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.