Square Roots and Properties of Exponents

The video tutorial explains how to simplify square roots, assuming all variables are non-negative. It provides examples, including the square roots of 16, p squared, 25y squared, and 121x squared. The tutorial demonstrates the process of simplifying these expressions by identifying factors and using properties of multiplication. The concept of a radicand is introduced, and the square root is described as the inverse of squaring.

What is the basic principle used to simplify square roots?

• The square root of a number is always positive.

• The square root of a number squared is the number itself.

• The square root of a number is always negative.

• The square root of a number is the number divided by two.

What is the square root of 16?

• 5

• 3

• 4

• 2

Why does the square root of p squared simplify to p?

• Because p is a constant.

• Because p squared is always negative.

• Because squaring p gives the radicand p squared.

• Because p is always positive.

What is the radicand in the expression √(p²)?

• 2p

• p²

• √p

• p

What is the square root of 25y squared?

• y

• 10y

• 5y

• 25y

How is the commutative property used in simplifying the square root of 25y squared?

• By adding terms together.

• By subtracting terms.

• By changing the order of multiplication.

• By dividing terms.

Which property allows us to rearrange terms in multiplication?

• Associative property

• Distributive property

• Commutative property

• Identity property

What is the square root of 121x squared?

• 11x

• x

• 121x

• 12x

Why is the square root of 121x squared equal to 11x?

• Because squaring 11x gives the radicand 121x squared.

• Because 11x is a constant.

• Because 11x is always negative.

• Because 11x is always positive.

What is the result of squaring 11x?

• 11x²

• 121x

• 11x

• 121x²