Math Problem Statement

√-36

Solution

The expression shown in the image is 36\sqrt{-36}.

Since the square root of a negative number is not defined in the set of real numbers, we must consider complex numbers. In the realm of complex numbers, the square root of a negative number involves the imaginary unit ii, where i=1i = \sqrt{-1}.

Thus:

36=36×1=6i\sqrt{-36} = \sqrt{36} \times \sqrt{-1} = 6i

So, the answer is 6i6i, where ii is the imaginary unit.

Would you like further details on this, or do you have any questions?

Here are five related questions to further explore this topic:

  1. What is the square root of other negative numbers like 25\sqrt{-25}?
  2. Can the square root of any negative number be simplified similarly?
  3. What is the definition of the imaginary unit ii?
  4. How do we perform operations (addition, multiplication, etc.) with imaginary numbers?
  5. Can real and imaginary numbers be combined in other ways to form complex numbers?

Tip: The square of the imaginary unit ii is i2=1i^2 = -1, which is fundamental in calculations involving complex numbers.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Square Roots
Imaginary Unit

Formulas

√-a = i√a, where i = √-1

Theorems

Imaginary Unit Theorem: i^2 = -1

Suitable Grade Level

Grades 9-12