Question

simplify and rewrite each square root as an imaginary number. use the keypad to enter the answers in the boxes. \\(\sqrt{-196} = \square\\) \\(\sqrt{-48} = \square\\) \\(\sqrt{-175} = \square\\)

Explanation:

Step1: Factor out -1 from radicand

$\sqrt{-196} = \sqrt{196 \times (-1)}$

Step2: Split into product of square roots

$\sqrt{196} \times \sqrt{-1}$

Step3: Evaluate and substitute $i=\sqrt{-1}$

$14i$

Step1: Factor out -1 from radicand

$\sqrt{-48} = \sqrt{16 \times 3 \times (-1)}$

Step2: Split into product of square roots

$\sqrt{16} \times \sqrt{3} \times \sqrt{-1}$

Step3: Evaluate and substitute $i=\sqrt{-1}$

$4\sqrt{3}i$

Step1: Factor out -1 from radicand

$\sqrt{-175} = \sqrt{25 \times 7 \times (-1)}$

Step2: Split into product of square roots

$\sqrt{25} \times \sqrt{7} \times \sqrt{-1}$

Step3: Evaluate and substitute $i=\sqrt{-1}$

$5\sqrt{7}i$

Answer:

$\sqrt{-196} = 14i$
$\sqrt{-48} = 4\sqrt{3}i$
$\sqrt{-175} = 5\sqrt{7}i$