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Arithmetic square root. Equation x² = a

The principal square root of a nonnegative number aa is the nonnegative number bb such that b2=ab^2=a. Notation: a\sqrt{a}. The equation x2=ax^2=a with a>0a>0 has two roots: x=±ax=\pm\sqrt{a}; the principal square root is the nonnegative one.
a≥0\sqrt{a}\ge0 always (in school a≥0a\ge0)
(a)2=a(\sqrt{a})^2=a, a2=∣a∣\sqrt{a^2}=|a|
When a=0a=0: x2=0⇒x=0x^2=0\Rightarrow x=0
Value of the principal square root.
Arithmetic square root (exact value)
64\sqrt{64}
=8=8
64=8, because 82=64, 8≥0\sqrt{64}=8\text{, because }8^2=64,\ 8\ge0
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