What is the square root of -20?

Understand the Problem

The question is asking for the square root of a negative number, which involves the concept of imaginary numbers. The square root of -20 can be expressed in terms of imaginary numbers as it is not a real number.

Answer

$2\sqrt{5}i$
Answer for screen readers

The square root of -20 is $2\sqrt{5}i$.

Steps to Solve

  1. Identify the square root of -20

Since we are looking for the square root of a negative number, we can express it using imaginary numbers. The square root of -20 can be rewritten as: $$ \sqrt{-20} = \sqrt{20} \cdot \sqrt{-1} $$

  1. Rewrite the square root of 20

Next, we simplify $$ \sqrt{20} $$: $$ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} $$

  1. Combine the results

Now we can combine our previous results to express $$ \sqrt{-20} $$: $$ \sqrt{-20} = 2\sqrt{5} \cdot i $$

The square root of -20 is $2\sqrt{5}i$.

More Information

The concept of imaginary numbers extends the real number system to account for the square roots of negative numbers. In this case, $i$ is defined as the imaginary unit, which satisfies $i^2 = -1$.

Tips

  • Ignoring the imaginary unit: It's important not to forget to include $i$ when dealing with the square roots of negative numbers.
  • Confusing real and imaginary solutions: Remember that there are no real solutions for the square roots of negative numbers.
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