Question

I have a test today can somebody help me with this question, please?

Answer 1

Answer:
`√(34)`

Work Shown:

`a^2+b^2 = c^2 \ \text{ ... pythagorean theorem}\\\\c = √(a^2+b^2)\\\\c = √(3^2+5^2)\\\\c = √(9+25)\\\\c = √(34)\\\\`

That cannot be simplified further because the prime factorization of 34 is 2*17, and neither of those factors are perfect squares.