Math Problem Statement

Find the square root of -20.

Solution

To find the square root of 20-20, we need to recognize that the square root of a negative number involves imaginary numbers, since the square of any real number is non-negative.

The square root of 20-20 can be expressed as:

20=1×20=i×20\sqrt{-20} = \sqrt{-1} \times \sqrt{20} = i \times \sqrt{20}

Where ii is the imaginary unit (i.e., i=1i = \sqrt{-1}).

Now, simplifying 20\sqrt{20}:

20=4×5=4×5=25\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}

Thus, the square root of 20-20 is:

20=2i5\sqrt{-20} = 2i\sqrt{5}

So, the answer is:

2i5\boxed{2i\sqrt{5}}

Would you like further explanation or details on this topic?

Here are some related questions for further exploration:

  1. What are imaginary numbers, and how are they used in math?
  2. How do you simplify expressions involving square roots of negative numbers?
  3. What is the geometric interpretation of complex numbers?
  4. Can you multiply or divide complex numbers in polar form?
  5. How do you solve quadratic equations that have complex solutions?

Tip: When dealing with square roots of negative numbers, always remember to introduce the imaginary unit i=1i = \sqrt{-1}.

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Math Problem Analysis

Mathematical Concepts

Square roots
Imaginary numbers
Simplifying radicals

Formulas

√(-a) = i√a
√(ab) = √a × √b

Theorems

Properties of square roots
Introduction to complex numbers

Suitable Grade Level

Grades 9-12