Simplifying Radicals and Operations

This video tutorial covers the unit on radicals and rational exponents, focusing on operations with radicals. It begins with simplifying square roots using factor trees, followed by examples of simplifying the square roots of 20 and 72. The tutorial then explains how to add and subtract radicals, emphasizing the need for like radicands. It also covers multiplying radicals using the 'outside times outside, inside times inside' rule. Finally, it discusses dividing radicals and the importance of rationalizing denominators.

What is the simplified form of the square root of 20?

• 10

• 5√2

• 4√5

• 2√5

When simplifying the square root of 72, which pair of numbers is taken out of the radical?

• 2 and 4

• 3 and 4

• 2 and 3

• 3 and 5

What must be true for two radicals to be added together?

• They must have the same coefficients.

• They must have the same radicands.

• They must be perfect squares.

• They must be prime numbers.

If you have -7√3 and -12√3, what is the result when you combine them?

• -19√3

• -5√3

• 5√3

• 19√3

How do you simplify the expression √8 + 5√2 + √18?

• 15√2

• 12√2

• 10√2

• 7√2

What is the rule for multiplying radicals?

• Add the coefficients, multiply the radicands

• Inside times inside, outside times outside

• Multiply the coefficients, add the radicands

• Divide the coefficients, multiply the radicands

What is the simplified form of 4√2 * 3√6?

• 12√12

• 24√3

• 12√6

• 24√6

What is the result of multiplying 6√3 by 5√6?

• 30√6

• 90√2

• 90√3

• 30√18

What is a key rule when dividing radicals?

• Radicals must be multiplied by the numerator.

• Radicals must be removed from the denominator.

• Radicals can remain in the denominator.

• Radicals must be added to the numerator.

How do you simplify the division of √14 by √2?

• 2√7

• 7

• √7

• 14