Simplifying Radicals with Variables

This video tutorial explains how to handle square roots involving variables with exponents. It covers the basic rule for even exponents, where the exponent is divided by two, and demonstrates this with examples. The video also addresses cases with coefficients and odd exponents, showing how to break them down for simplification. Through various examples, the tutorial provides a comprehensive understanding of managing square roots with different types of exponents.

What is the rule for finding the square root of a variable with an even exponent?

• Divide the exponent by 2

• Subtract 2 from the exponent

• Multiply the exponent by 2

• Add 2 to the exponent

What is the square root of x^2?

• x

• 2x

• x^1/2

• x^2

What is the square root of m^6?

• m^1/3

• m^6

• m^2

• m^3

If you have a coefficient in front of the variable, how do you handle it?

• Divide the coefficient by 2

• Multiply the coefficient by 2

• Ignore the coefficient

• Take the square root of the coefficient

What is the square root of 9k^2?

• 3k^2

• k^3

• 9k

• 3k

How do you handle the square root of a variable with an odd exponent?

• Subtract 1 from the exponent

• Divide the exponent by 2

• Break the exponent into an even part and an odd part

• Multiply the exponent by 2

What is the square root of y^5?

• y^2√y

• y^3

• y^2

• y^5

What is the square root of a^2b^3?

• ab^3

• a^2b^2

• ab√b

• a^2b

What is the square root of x^2y^3z^4?

• xyz^2

• x^2y^3z^4

• xy^2z^2√y

• x^2y^2z

What is the square root of 144k^3?

• 12k^3

• 12k^2

• 12k

• 12k√k