Simplifying Square Roots and Exponents

The video tutorial explains how to simplify fractions where both the numerator and denominator are square roots. It demonstrates the process through two examples, showing how to rewrite the expression as a single square root, simplify the fraction, and identify perfect square factors. The tutorial emphasizes the importance of breaking down numbers into prime factors and grouping equal factors to simplify the expression.

What is the first step in simplifying fractions where both the numerator and denominator are square roots?

• Subtract the numerator from the denominator.

• Rewrite the expression as the square root of a single fraction.

• Add the numerator and denominator.

• Multiply the numerator and denominator by the same number.

In the first example, what is the result of dividing 200 by 2?

• 200

• 100

• 50

• 150

How do you simplify x^9 divided by x^5?

• x^3

• x^2

• x^5

• x^4

What is the square root of 100?

• 15

• 10

• 20

• 5

In the second example, what is the result of dividing 735 by 5?

• 145

• 150

• 147

• 149

How do you simplify x^11 divided by x^6?

• x^3

• x^4

• x^6

• x^5

What are the prime factors of 147?

• 5 and 29

• 7 and 21

• 3 and 49

• 2 and 73

What is the simplified form of the square root of 3 x 7 x 7?

• 7√3

• 3√7

• √21

• 21

How is x^5 expressed in terms of perfect square factors?

• x^4 x x

• x^2 x x^2 x x

• x^2 x x^3

• x^3 x x^2

What is the final simplified form of the expression in the second example?

• 7x^2 x √3

• 7x x √3x

• 7x x √3

• 7x^2 x √3x