Question
Multiply. Assume m is greater than or equal to zero, and write your answer in simplest form.
square root of 3m2*square root of 3
square root of 3m2*square root of 3
Answers
GPT-4o mini
To multiply the expressions \(\sqrt{3m^2}\) and \(\sqrt{3}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).
Thus we can write:
\[
\sqrt{3m^2} \cdot \sqrt{3} = \sqrt{3m^2 \cdot 3}
\]
Next, we can multiply the terms inside the square root:
\[
= \sqrt{3 \cdot 3 \cdot m^2} = \sqrt{9m^2}
\]
Now, we can simplify \(\sqrt{9m^2}\):
\[
\sqrt{9m^2} = \sqrt{9} \cdot \sqrt{m^2} = 3m
\]
Therefore, the final answer is:
\[
3m
\]
Thus we can write:
\[
\sqrt{3m^2} \cdot \sqrt{3} = \sqrt{3m^2 \cdot 3}
\]
Next, we can multiply the terms inside the square root:
\[
= \sqrt{3 \cdot 3 \cdot m^2} = \sqrt{9m^2}
\]
Now, we can simplify \(\sqrt{9m^2}\):
\[
\sqrt{9m^2} = \sqrt{9} \cdot \sqrt{m^2} = 3m
\]
Therefore, the final answer is:
\[
3m
\]