Simplifying Square Roots and Exponent Expressions

The video tutorial explains how to simplify the expression 3 times the principal root of 500x^3. It begins by breaking down the components under the radical sign into perfect squares and non-perfect squares. The process involves prime factorization and rewriting the expression using exponent properties. The tutorial emphasizes the importance of considering the absolute value when dealing with square roots of squared variables. The final simplified expression is presented as 30 times the absolute value of x times the square root of 5x.

What is the first step in simplifying the principal root of 500x to the third power?

• Multiply all terms by 3.

• Divide all terms by 5.

• Combine all terms under the radical sign.

• Break down the terms into perfect squares.

What is the prime factorization of 500?

• 2^3 * 5^3

• 2^2 * 5^2 * 5

• 2^2 * 5^3

• 2^3 * 5^2

Which of the following is a perfect square?

• 25

• 50

• 5

• 10

How can x to the third power be rewritten to include a perfect square?

• x^3 = x^2 + x

• x^3 = x^2 * x

• x^3 = x * x * x

• x^3 = x^2 - x

What is the principal root of 10 squared?

• 15

• 10

• 5

• 20

Why do we use the absolute value of x when taking the square root of x squared?

• To make the calculation easier.

• To avoid negative numbers.

• To simplify the expression.

• To ensure the result is always positive.

What is the principal root of 100?

• 20

• 15

• 10

• 5

What is the simplified form of 3 times the principal root of 500x to the third power?

• 30 * x * sqrt(5x)

• 30 * |x| * sqrt(5x)

• 3 * |x| * sqrt(5x)

• 30 * x * sqrt(5)

What is the result of multiplying 3, 10, and the absolute value of x?

• 3 * 10 * x

• 30 * x

• 3 * 10 * |x|

• 30 * |x|

How can the product of sqrt(5) and sqrt(x) be rewritten?

• sqrt(5) + sqrt(x)

• 5 * sqrt(x)

• sqrt(5) * x

• sqrt(5x)