Question

question 7
simplify.
$3\sqrt{-50}$
$\bigcirc\\ 15\sqrt{2}$
$\bigcirc\\ 15i\sqrt{2}$
$\bigcirc\\ -15i\sqrt{2}$
$\bigcirc\\ -15\sqrt{2}$

Explanation:

Step1: Recall Imaginary Unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \), so we can rewrite \( \sqrt{-50} \) as \( \sqrt{50 \times (-1)} \).

Step2: Simplify Square Root

Using the property \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (for \( a \geq 0, b \geq 0 \); here we extend to imaginary numbers), we have \( \sqrt{-50} = \sqrt{50} \times \sqrt{-1} = \sqrt{25 \times 2} \times i = 5\sqrt{2}i \).

Step3: Multiply by Coefficient

Now, multiply by the coefficient 3: \( 3 \times 5\sqrt{2}i = 15i\sqrt{2} \).

Answer:

B. \( 15i\sqrt{2} \) (assuming the second option is labeled B; if the options are labeled as given with the second option being \( 15i\sqrt{2} \), then the answer is that option)