Question

Could somebody please provide me wish an explaination for the textbook example answers:

a) why here is 3 and 4 relevant and what do them being a square number have to do with it?
b) I understand this one
c) why is 5 square rooted ​

Answer 1

`\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ 9p^2-16q^2\implies 3^2p^2-4^2q^2\implies (3p)^2-(4q)^2\implies (3p-4q)(3p+4q) \\\\[-0.35em] ~\dotfill\\\\ x^2-5\implies (x)^2-√(5^2)\implies (x)^2-(√(5))^2\implies (x-√(5))(x+√(5))`

Answer 2

Explanation:

The number 5 is prime. This implies that the number 5 is pairless and is not in the power of 2. Therefore, the square root of 5 is irrational.

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