Math / Numbers & Operations

QuestionSimplify by factoring. $\sqrt{63}$ $\sqrt{63}=\square$ (Type an exact an as needed.)

Studdy Solution

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 $3 \times 3 \times 7$ .

STEP 4

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: $\boxed{3\sqrt{7}}$

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