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Write sqrt(-125) in simplest radical form. Answer:

Write −125 \sqrt{-125} in simplest radical form.\newlineAnswer:

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Full solution

Q. Write −125 \sqrt{-125} in simplest radical form.\newlineAnswer:
  1. Split into Product: Express −125\sqrt{-125} as the product of square roots and −1\sqrt{-1}.−125=−1×125=−1×125\sqrt{-125} = \sqrt{-1 \times 125} = \sqrt{-1} \times \sqrt{125}
  2. Express as Complex Number: Express −1×125\sqrt{-1} \times \sqrt{125} as a complex number by using ii.−125=−1×125=i×125\sqrt{-125} = \sqrt{-1} \times \sqrt{125} = i \times \sqrt{125}
  3. Factor and Simplify: Simplify 125\sqrt{125} by factoring it into 25×5\sqrt{25 \times 5}.125=25×5=25×5=5×5\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5 \times \sqrt{5}
  4. Combine Results: Combine the results to express −125\sqrt{-125} in simplest radical form.−125=i×5×5=5i×5\sqrt{-125} = i \times 5 \times \sqrt{5} = 5i \times \sqrt{5}

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