Math Problem Statement

Simplify √(-10).

Solution

The expression in the image is asking to simplify 10\sqrt{-10}.

This involves a negative number under the square root, which is not a real number. In mathematics, the square root of a negative number introduces imaginary numbers.

To simplify:

10=1×10=i10\sqrt{-10} = \sqrt{-1} \times \sqrt{10} = i\sqrt{10}

Where ii is the imaginary unit, defined as i=1i = \sqrt{-1}.

Thus, the simplified form is i10i\sqrt{10}.

Would you like further details or have any questions?

Here are five related questions for further exploration:

  1. How do you simplify the square root of other negative numbers?
  2. What is the significance of the imaginary unit ii in complex numbers?
  3. How do you add or subtract imaginary numbers?
  4. How can we represent complex numbers in the polar form?
  5. How do complex numbers appear in real-world applications?

Tip: Whenever you see a negative number inside a square root, think of using imaginary numbers, since real square roots only apply to non-negative numbers.

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Square Roots

Formulas

√(-x) = i√x
i = √(-1)

Theorems

Properties of square roots of negative numbers
Imaginary unit definition

Suitable Grade Level

Grades 9-12