Math Problem Statement

What is the simplified form of the square root of -24?

Solution

The expression in the image is 24\sqrt{-24}.

This is an example of a square root of a negative number, which involves complex numbers. The square root of a negative number can be rewritten using the imaginary unit ii, where i=1i = \sqrt{-1}.

We can express this as: 24=1×24=1×24=i×24\sqrt{-24} = \sqrt{-1 \times 24} = \sqrt{-1} \times \sqrt{24} = i \times \sqrt{24} Now, simplifying 24\sqrt{24}: 24=4×6=4×6=26\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} Thus, the final simplified form is: 24=2i6\sqrt{-24} = 2i\sqrt{6}

Would you like further details or have any other questions?

Here are five related questions:

  1. How do you simplify square roots of negative numbers generally?
  2. What is the significance of the imaginary unit ii in complex numbers?
  3. How do you simplify radicals like 24\sqrt{24}?
  4. What are some applications of complex numbers in physics or engineering?
  5. How do you add or subtract complex numbers?

Tip: When simplifying square roots of negative numbers, always factor out 1\sqrt{-1} as ii first.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Numbers
Simplifying Radicals

Formulas

√(-a) = i√a
√(ab) = √a * √b

Theorems

Definition of the Imaginary Unit i, where i = √(-1)

Suitable Grade Level

Grades 9-12