Simplifying Radical Expressions and Rationalizing Denominators

The video tutorial covers factoring numbers, understanding and simplifying square roots, and rationalizing denominators. It explains prime factorization, the nature of irrational numbers, and methods to simplify square roots. The tutorial also details steps to rationalize denominators in fractions, including using conjugates for binomial denominators.

What is the prime factorization of 72?

• 2^4 * 3

• 2^3 * 3^2

• 2^2 * 3^3

• 2 * 3^3

Which of the following is an example of an irrational number?

• 9

• 16

• 4

• √5

How do you simplify the square root of 124?

• 2√62

• 2√31

• 4√31

• √62

What is the simplified form of √5 * √18?

• 2√45

• 3√10

• √90

• 5√9

When simplifying square roots, what do you do with pairs of prime factors?

• Leave them inside the radical

• Divide them by 2

• Take them out of the radical as a single factor

• Multiply them by 2

What is the first step in rationalizing the denominator of a fraction?

• Multiply the numerator and the denominator by the radical in the denominator

• Multiply the numerator by the denominator

• Subtract the numerator from the denominator

• Add the numerator and the denominator

What is the simplified form of 5/√10?

• √10/5

• 5√10

• 5√10/10

• √10/2

How do you simplify the fraction 56/45 under a square root?

• √(56/45)

• √56/√45

• √(7*8)/√(3*15)

• √(7*8)/√(3*3*5)

What is the conjugate of 2√2 - 3?

• 2√2 + 3

• 2√2 - 3

• 3 - 2√2

• 3 + 2√2

What is the result of multiplying 5 by the conjugate of 2√2 - 3?

• 5√2 + 3

• 10√2 - 15

• 10√2 + 15

• 5√2 - 3