Simplify: $-6\sqrt{150r}$
Understand the Problem
The question is asking to simplify the expression $-6\sqrt{150r}$. This involves factoring out perfect squares from under the radical to simplify the expression.
Answer
$-30\sqrt{6r}$
Answer for screen readers
$-30\sqrt{6r}$
Steps to Solve
- Factor the number under the square root
First, we need to factor 150 to find any perfect square factors. $150 = 25 \times 6 = 5^2 \times 6$
- Rewrite the expression using the factored form
Now we can rewrite the original expression as: $-6\sqrt{150r} = -6\sqrt{25 \times 6 \times r}$
- Simplify the square root
We take the square root of 25, which is 5, and move it outside the square root: $-6\sqrt{25 \times 6 \times r} = -6 \times 5 \sqrt{6r}$
- Multiply the numbers outside the square root
Finally, we multiply $-6$ and $5$: $-6 \times 5 \sqrt{6r} = -30\sqrt{6r}$
$-30\sqrt{6r}$
More Information
The simplified expression $-30\sqrt{6r}$ is equivalent to the original expression $-6\sqrt{150r}$.
Tips
A common mistake is not fully factoring the number under the square root, which would result in not simplifying the expression completely. Another common mistake is incorrectly multiplying the terms outside of the radical or incorrectly simplifying the square root.
AI-generated content may contain errors. Please verify critical information
