Math Problem Statement

Simplify √-10.

Solution

The expression shown in the image is 10\sqrt{-10}. This is the square root of a negative number, which means the solution involves imaginary numbers.

To simplify 10\sqrt{-10}:

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

So, the simplified form of 10\sqrt{-10} is:

i10i\sqrt{10}

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

Would you like more details or have any questions?

Here are 5 related questions for further practice:

  1. What is 25\sqrt{-25}?
  2. How do you simplify 36\sqrt{-36}?
  3. What is the value of i2i^2 in complex numbers?
  4. How do you add 9\sqrt{-9} and 4\sqrt{-4}?
  5. What is the simplified form of 202\frac{\sqrt{-20}}{2}?

Tip: When working with square roots of negative numbers, always remember that they result in imaginary numbers, involving the unit ii.

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Square Roots

Formulas

√(-x) = i√x where i = √(-1)
√(-10) = i√10

Theorems

Imaginary Unit Definition (i = √(-1))

Suitable Grade Level

Grades 9-12