Answer :
Let's simplify the given radical [tex]\(\sqrt{300}\)[/tex] and then compare it to the provided answer choices.
Step 1: Start by simplifying the radicand inside the square root.
[tex]\[ 300 \][/tex]
Step 2: Factorize [tex]\(300\)[/tex] into its prime factors:
[tex]\[ 300 = 2^2 \cdot 3 \cdot 5^2 \][/tex]
Step 3: Use the property of square roots that states [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex]. Break down the square root:
[tex]\[ \sqrt{300} = \sqrt{2^2 \cdot 3 \cdot 5^2} \][/tex]
Step 4: Separate the factors under the square root:
[tex]\[ \sqrt{300} = \sqrt{2^2} \cdot \sqrt{3} \cdot \sqrt{5^2} \][/tex]
Step 5: Simplify the square roots of the perfect squares:
[tex]\[ \sqrt{2^2} = 2 \][/tex]
[tex]\[ \sqrt{5^2} = 5 \][/tex]
Step 6: Combine the simplified factors:
[tex]\[ \sqrt{300} = 2 \cdot 5 \cdot \sqrt{3} = 10 \sqrt{3} \][/tex]
Having simplified [tex]\(\sqrt{300}\)[/tex], we have:
[tex]\[ \sqrt{300} = 10 \sqrt{3} \][/tex]
Now let's compare the simplified expression with the provided answer choices:
A. [tex]\(3 \sqrt{10}\)[/tex]
B. [tex]\(2 \sqrt{75}\)[/tex]
C. [tex]\(5 \sqrt{12}\)[/tex]
D. [tex]\(10 \sqrt{3}\)[/tex]
From our simplification, we can see that [tex]\(\sqrt{300} = 10 \sqrt{3}\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
Step 1: Start by simplifying the radicand inside the square root.
[tex]\[ 300 \][/tex]
Step 2: Factorize [tex]\(300\)[/tex] into its prime factors:
[tex]\[ 300 = 2^2 \cdot 3 \cdot 5^2 \][/tex]
Step 3: Use the property of square roots that states [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex]. Break down the square root:
[tex]\[ \sqrt{300} = \sqrt{2^2 \cdot 3 \cdot 5^2} \][/tex]
Step 4: Separate the factors under the square root:
[tex]\[ \sqrt{300} = \sqrt{2^2} \cdot \sqrt{3} \cdot \sqrt{5^2} \][/tex]
Step 5: Simplify the square roots of the perfect squares:
[tex]\[ \sqrt{2^2} = 2 \][/tex]
[tex]\[ \sqrt{5^2} = 5 \][/tex]
Step 6: Combine the simplified factors:
[tex]\[ \sqrt{300} = 2 \cdot 5 \cdot \sqrt{3} = 10 \sqrt{3} \][/tex]
Having simplified [tex]\(\sqrt{300}\)[/tex], we have:
[tex]\[ \sqrt{300} = 10 \sqrt{3} \][/tex]
Now let's compare the simplified expression with the provided answer choices:
A. [tex]\(3 \sqrt{10}\)[/tex]
B. [tex]\(2 \sqrt{75}\)[/tex]
C. [tex]\(5 \sqrt{12}\)[/tex]
D. [tex]\(10 \sqrt{3}\)[/tex]
From our simplification, we can see that [tex]\(\sqrt{300} = 10 \sqrt{3}\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
