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
- 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: $$ \sqrt{-20} = \sqrt{20} \cdot \sqrt{-1} $$
- Rewrite the square root of 20
Next, we simplify $$ \sqrt{20} $$: $$ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} $$
- 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.
