Question

simplifying radicals with negative radicands
score: 1/5 penalty: 0.25 off
question
write $sqrt{-175}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Separate negative radicand

$\sqrt{-175} = \sqrt{-1 \times 175}$

Step2: Rewrite using imaginary unit $i$

$\sqrt{-1 \times 175} = i\sqrt{175}$

Step3: Factor 175 into perfect square

$i\sqrt{25 \times 7}$

Step4: Simplify the radical

$i\sqrt{25} \times \sqrt{7} = 5i\sqrt{7}$

Answer:

$5i\sqrt{7}$