Simplifying Expressions with Imaginary Numbers

This video tutorial explains how to simplify radicals with negative radicands. It covers the properties of radicals, including the handling of negative radicands by separating the negative part as the square root of negative one, represented by 'i'. The tutorial provides several examples, demonstrating step-by-step simplification of radicals and multiplication of complex numbers. It concludes with an example resembling the quadratic formula, emphasizing the importance of understanding the properties of 'i' and negative radicands.

What is the part of a radical expression that is located inside the radical sign called?

• Exponent

• Coefficient

• Radicand

• Index

What is the term for the number outside the radical sign?

• Radicand

• Exponent

• Index

• Base

Which property of square roots is only valid for real numbers?

• The square root of a times the square root of b equals the square root of a times b

• The square root of a plus the square root of b equals the square root of a plus b

• The square root of a divided by the square root of b equals the square root of a divided by b

• The square root of a minus the square root of b equals the square root of a minus b

How should you handle negative radicands when simplifying square roots?

• Separate the negative part as the square root of -1

• Combine them directly

• Add them to the index

• Ignore the negative sign

What is the simplified form of the square root of -108?

• 12 times the square root of 1i

• 9 times the square root of 2i

• 3 times the square root of 6i

• 6 times the square root of 3i

Which of the following is a perfect square factor of 108?

• 3

• 54

• 9

• 27

What is the simplified form of the square root of -8?

• 2 times the square root of 2i

• 4 times the square root of 2i

• 3 times the square root of 2i

• 5 times the square root of 2i

What is the simplified form of the square root of -18?

• 6 times the square root of 1i

• 4 times the square root of 2i

• 3 times the square root of 2i

• 2 times the square root of 3i

What is the result of multiplying i by itself?

• 0

• i

• -1

• 1

What is the simplified result of multiplying 2 times the square root of 2i by 3 times the square root of 2i?

• -6

• 6

• -12

• 12