Question

question
express in simplest radical form.
\sqrt{63}

Explanation:

Step1: Factor the radicand

Factor 63 into prime factors: $63 = 9\times7$.

Step2: Apply the square - root property

We know that $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a\geq0,b\geq0$). So $\sqrt{63}=\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}$.

Step3: Simplify the square root of a perfect square

Since $\sqrt{9} = 3$, then $\sqrt{9}\times\sqrt{7}=3\sqrt{7}$.

Answer:

$3\sqrt{7}$