Simplifying Radicals with Variables: A Deep Dive

What is the first step in simplifying radicals with variables?

• Identify the radicand's prime factors

• Bring pairs of variables outside the radical

• Multiply factors inside the radical

• Simplify the expression outside the radical

In the expression sqrt(40x^3y^4), what is the prime factorization of 40?

• 2x2x2x5

• 4x10

• 2x5x4

• 2x20

How many y variables come outside the radical in sqrt(40x^3y^4)?

• Four

• Two

• Three

• One

What remains inside the radical after simplification of sqrt(40x^3y^4)?

• 2x

• 5x

• 10x

• 5

What is the simplified form of sqrt(121a^2b^2)?

• 11ab

• 11

• 11a^2b^2

• 121ab

In the expression sqrt(60r^3s^2t^4), what is the prime factorization of 60?

• 6x10

• 3x20

• 2x2x3x5

• 2x30

How many t variables come outside the radical in sqrt(60r^3s^2t^4)?

• One

• Three

• Two

• Four

What is left inside the radical after simplifying sqrt(60r^3s^2t^4)?

• 3s

• 15r

• 5r

• 3r

What is the coefficient of r in the final expression of sqrt(60r^3s^2t^4)?

• 1

• 2

• 3

• 4

Which of the following is a correct step in simplifying radicals with variables?

• All numbers stay inside the radical

• Pairs of numbers and variables come outside the radical

• Only variables come outside the radical

• Variables are not affected by the radical