Exploring Radicals with Variables

What does the square root of 36 simplify to?

• 6

• 36

• 18

• 3

How is the square root of 8 simplified using the factor tree method?

• 2 times 2

• 2 times the square root of 2

• 8

• 4

What is the result of simplifying the square root of 36n?

• 6 times the square root of n

• 6n

• The square root of 36 times n

• 36n

How do you simplify the square root of 72x squared?

• 6x times the square root of 2

• 8x squared

• 72x

• 6 times the square root of 72x

What is the result of simplifying the square root of 72 using prime factorization?

• 12

• 36

• 72

• 6 times the square root of 2

What is the simplified form of the square root of 27x to the fourth y to the third z to the seventh?

• The square root of 27x4y3z7

• 9x squared yz cubed times the square root of 3yz

• 27xyz

• 9x squared yz cubed

When simplifying radicals with variables, what happens to variables with exponents that have a remainder when divided by the root?

• The variable is discarded.

• The remainder determines the exponent of the variable inside the radical.

• The variable moves entirely outside the radical.

• The remainder is ignored.

What is the purpose of dividing the exponent by the root when simplifying radicals with variables?

• None of the above.

• To find the new exponent for the variable inside the radical.

• To increase the complexity of the problem.

• To determine how many times the variable will be placed outside the radical.

In the expression 27x to the fourth y to the third z to the seventh, what is the simplified form outside the radical?

• 9x squared yz cubed

• 27x4y3z7

• 9x4y3z7

• 27xyz

What is the simplified form of the square root of 3y in the context of the expression 27x to the fourth y to the third z to the seventh?

• 3y

• 3

• The square root of 3y

• y