Question
radical 10v^4 times radical 3
Answers
GPT-4o mini
To simplify the expression \( \sqrt{10v^4} \times \sqrt{3} \), you can use the property of square roots that states:
\[
\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
\]
Applying this property, we have:
\[
\sqrt{10v^4} \times \sqrt{3} = \sqrt{10v^4 \times 3} = \sqrt{30v^4}
\]
Now, to simplify \( \sqrt{30v^4} \):
1. \( v^4 \) under the square root simplifies to \( v^2 \), since \( \sqrt{v^4} = v^{4/2} = v^2 \).
2. The \( \sqrt{30} \) remains as is, since 30 cannot be simplified further.
Therefore, the final result is:
\[
\sqrt{30} \cdot v^2
\]
Combining these, the simplified expression is:
\[
v^2 \sqrt{30}
\]
\[
\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
\]
Applying this property, we have:
\[
\sqrt{10v^4} \times \sqrt{3} = \sqrt{10v^4 \times 3} = \sqrt{30v^4}
\]
Now, to simplify \( \sqrt{30v^4} \):
1. \( v^4 \) under the square root simplifies to \( v^2 \), since \( \sqrt{v^4} = v^{4/2} = v^2 \).
2. The \( \sqrt{30} \) remains as is, since 30 cannot be simplified further.
Therefore, the final result is:
\[
\sqrt{30} \cdot v^2
\]
Combining these, the simplified expression is:
\[
v^2 \sqrt{30}
\]