Simplify. sqrt(36) ______

Prime Factorization: To simplify the square root of 12, we first need to find the prime factorization of the number under the radical. Prime factorization of 12 is 2 * 2 * 3, which can be written as 2^2 * 3.Rewriting the Square Root: Now, we can rewrite the square root of 12 using its prime factors. sqrt(12) = sqrt(2^2 * 3)Applying the Product Property: Next, we apply the product property of square roots, which allows us to take the square root of each factor separately. sqrt(2^2 * 3) = sqrt(2^2) * sqrt(3)Simplifying the Square Root: Since the square root of a square number is just the base of the square, we can simplify sqrt(2^2) to 2. sqrt(2^2) * sqrt(3) = 2 * sqrt(3)Final Simplified Form: Therefore, the simplified form of sqrt(12) is 2sqrt(3).

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Simplify. $\newline$ $\sqrt{36}$ $\newline$ _____

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{36}

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_____

Identify prime factors: $\sqrt{36}$ $\newline$ First, we need to identify the prime factors of the number under the square root, which is $36$ in this case. $\newline$ However, since $36$ is a perfect square, we know that its square root will be a whole number. $\newline$ $\sqrt{36} = \sqrt{6 \times 6}$
Simplify perfect square: $\sqrt{6 \times 6}$ $\newline$ Now, we can simplify the square root of a perfect square by taking the square root of each factor. $\newline$ $\sqrt{6 \times 6} = \sqrt{6^2}$
Cancel square root and square: $\sqrt{6^2}$ $\newline$ The square root and the square cancel each other out, so we are left with just the base of the exponent. $\newline$ $\sqrt{6^2} = 6$