Simplifying Radicals: Key Concepts and Techniques

The video tutorial explains how to simplify square roots by factoring the radicand into prime factors. It demonstrates the process using examples of square roots of 24, 48, and 90, including cases with coefficients. The tutorial emphasizes finding matching pairs of factors to simplify the expression and provides step-by-step guidance on handling coefficients outside the radical.

What is the first step in simplifying the square root of 24?

• Write the number in expanded form

• Identify the radicand

• Factor the number completely

• Divide by 2 repeatedly

What does the 'index' refer to in the context of radicals?

• The base number in a pair

• The imaginary number used in simplification

• The number inside the radical

• The number of times you can divide

How many pairs of twos are found when simplifying the square root of 24?

• Four pairs

• Three pairs

• One pair

• Two pairs

What is the simplified form of the square root of 24?

• 2 root 6

• 4 root 6

• 2 root 12

• 6 root 4

When simplifying the square root of 48 with a coefficient, how many pairs of twos are pulled out?

• One pair

• Four pairs

• Two pairs

• Three pairs

What is the final simplified form of the square root of 48?

• 4 root 3

• 8 root 3

• 16 root 3

• 12 root 3

What factor pair is used to simplify the radical of 90?

• Pair of fours

• Pair of threes

• Pair of twos

• Pair of fives

What is left inside the radical after simplifying the square root of 90?

• Radical 15

• Radical 2

• Radical 5

• Radical 10

What is the final simplified form of the square root of 90?

• 9 root 15

• 9 root 10

• 9 root 5

• 9 root 2

How does the coefficient affect the final simplified form of a radical?

• It is multiplied with the number outside the radical

• It is added to the number outside the radical

• It is subtracted from the number outside the radical

• It does not affect the simplification