Math Problem Statement

Write √(-10) in simplest radical form.

Solution

To simplify 10\sqrt{-10}, we must recognize that the square root of a negative number involves imaginary numbers. The square root of any negative number can be expressed in terms of ii, where ii is the imaginary unit and i=1i = \sqrt{-1}.

Here's how we handle this:

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

Thus, the simplest radical form of 10\sqrt{-10} is:

i10i\sqrt{10}

Let me know if you would like further details or have any questions!


Here are five related questions to expand your understanding:

  1. How do you simplify the square root of any negative number?
  2. What are the properties of the imaginary unit ii?
  3. Can you simplify expressions like 25\sqrt{-25}?
  4. How are complex numbers represented in the form a+bia + bi?
  5. How do you add and subtract complex numbers?

Tip: Always remember that 1\sqrt{-1} is defined as the imaginary unit ii, and it is the key to simplifying square roots of negative numbers.

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Square Roots
Radicals

Formulas

√(-a) = i√a where a > 0
√(-1) = i

Theorems

Definition of the Imaginary Unit

Suitable Grade Level

Grades 9-11