Question

How many square roots does each square number have?Why?

Answer 1

every positive numbers have 2 square roots -√a and the other √a.

Answer 2

Each square number has two square roots.

Reason: It happens because when we multiply the positive square root by itself, we get the square number, and this is the same for the negative square root.

Explanation:

• Let us take a square number A, whose two square roots are p and q, where they can be either positive or negative, but not both.

• A has two square roots. They are $(+\sqrt{A})$ and $(-\sqrt{A})$.

• From our assumption, we can write:

1. $p=+\sqrt{A}\Rightarrow p^{2}=A$
2. $q=-\sqrt{A}\Rightarrow q^{2}=A$

• We have used the multiplication rule for symbols: (+)(+) = (+) and (-)(-) = (+).

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