Surds, Rationalizing Denominators, and Applying Laws of Surds

The video tutorial explains surds, which are expressions containing irrational square roots. It covers two main laws of surds: multiplication and division, emphasizing that you can multiply or divide the values under the root. The tutorial also warns against common mistakes when adding surds. It demonstrates how to express surds in the form a√b by identifying square factors. Finally, it explains rationalizing the denominator by multiplying by the conjugate to eliminate irrational roots.

What is the result of multiplying √3 by √7?

• √21

• √10

• √30

• √49

Which of the following is a correct simplification of √6 divided by √10?

• √1.6

• √60

• √3/5

• √16

How can √200 be expressed in the form a√b?

• 2√100

• 10√2

• 20√5

• 5√40

What is the process of removing an irrational root from the denominator called?

• Simplifying the numerator

• Rationalizing the denominator

• Multiplying by the root

• Adding the conjugate

When rationalizing a denominator with an expression like 3 + √2, what should you multiply by?

• 3 + √2

• 3 - √2

• √2

• 3