Math Snap

STEP 1

1. We need to simplify $\sqrt{63}$ by factoring.
2. We are looking for an exact answer, not a decimal approximation.

STEP 2

1. Identify the prime factors of 63.
2. Simplify the square root using the prime factors.

STEP 3

Identify the prime factors of $63$.
First, divide by the smallest prime number, $3$:
$$63 \div 3 = 21$$ Next, factor $21$ by dividing by $3$ again:
$$21 \div 3 = 7$$ Since $7$ is a prime number, the prime factors of $63$ are $3 \times 3 \times 7$.

Simplify $\sqrt{63}$ using the prime factors.
Write $\sqrt{63}$ in terms of its prime factors:
$$\sqrt{63} = \sqrt{3 \times 3 \times 7}$$ Apply the property of square roots that allows us to separate the factors:
$$\sqrt{63} = \sqrt{3^2 \times 7}$$ Since $\sqrt{3^2} = 3$, we can simplify further:
$$\sqrt{63} = 3\sqrt{7}$$ The simplified form of $\sqrt{63}$ is:
$$\boxed{3\sqrt{7}}$$