Question

write the number as the product of a real number and ( i ).
( sqrt{-125} )

( sqrt{-125} = square )
(simplify your answer. type your answer in the form ( a + bi ). type an exact answer, using radicals

Explanation:

Step1: Rewrite sqrt(-1) as i

$\sqrt{-125} = \sqrt{125 \times (-1)} = \sqrt{125} \times \sqrt{-1} = \sqrt{125}i$

Step2: Simplify sqrt(125)

$\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}$

Step3: Combine terms

$\sqrt{-125} = 5\sqrt{5}i$ (matches form $a+bi$ where $a=0$)

Answer:

$5\sqrt{5}i$