Simplifying Radicals with Variable Radicands

What is the general principle used to simplify radicals with variables?

• The nth root of a^n equals 1

• The nth root of a^n equals a^n

• The nth root of a^n equals n

• The nth root of a^n equals a

How many groups of three can be made from x^6 when simplifying the cube root?

• Three groups

• Two groups

• One group

• Four groups

What is the simplified form of the cube root of x^7?

• x^2 * cube root of x^2

• x^3 * cube root of x^2

• x^2 * cube root of x

• x^3 * cube root of x

When simplifying square roots, what multiples are we looking for in the exponents?

• Multiples of four

• Multiples of five

• Multiples of three

• Multiples of two

What is the simplified form of the square root of 32x^4y^9?

• 4x^2y^4 * square root of 2

• 4x^2y^4 * square root of y

• 4x^2y^4 * square root of 2y^2

• 4x^2y^4 * square root of 2y

What is the simplified form of the cube root of 216m^3n^6?

• 6m^2n^2

• 6mn^2

• 6m^2n

• 6mn

What is the simplified form of the cube root of 56r^8s^4?

• 2r^2s * cube root of 7s

• 2r^2s * cube root of 7r^2

• 2r^2s * cube root of 7r^2s^2

• 2r^2s * cube root of 7r^2s

What is the simplified form of the cube root of -64x^10y^21?

• -4x^3y^7 * cube root of x

• -4x^3y^7 * cube root of y^2

• -4x^3y^7 * cube root of x^2

• -4x^3y^7 * cube root of y

What is the simplified form of the cube root of -81p^2q^12?

• -3p^2q^4 * cube root of 3

• -3pq^4 * cube root of 3

• -3pq^4 * cube root of q

• -3pq^4 * cube root of p

What is the simplified form of the square root of 324a^3?

• 18a^1.5

• 18a^3

• 18a^1

• 18a^2