Exploring Nth Roots and Rational Exponents

What does the index number in a square root imply if not specified?

• It is always 2

• It is always 1

• It is always 3

• It can be any number

What is the result of the third root of -64?

• -8

• No solution

• 4

• -4

Tags

CCSS.HSA.REI.A.2

CCSS.HSN.CN.A.1

CCSS.HSN.RN.A.2

Why is there no solution for the fourth root of -81?

• Negative numbers do not have real fourth roots

• It is an imaginary number

• The calculation is incorrect

• It simplifies to 3

Tags

CCSS.HSN.CN.A.1

What does a rational exponent of 9 to the 3/2 power simplify to?

• 3

• 27

• 81

• 9

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CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

How can you simplify an expression with a negative exponent, like 4 to the -1/2 power?

• Square root of 4 in the denominator

• Square root of 4 in the numerator

• No simplification possible

• 4 in the numerator

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

What is the correct approach to solve the equation 5x^3 = 320?

• Divide by 5 and take the square root

• Multiply by 5 and take the square root

• Multiply by 5 and take the cube root

• Divide by 5 and take the cube root

When solving x + 5 to the fourth power equals 16, why must you consider both positive and negative solutions?

• Because it simplifies to zero

• Because it is a requirement for all equations

• Because the root is even

• Because the root is odd

Tags

CCSS.HSA.REI.A.2

What is the fifth root of 1024?

• 4

• 1024

• 32

• 10

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

How do you handle the equation 8x^3 = 64?

• Divide by 8 and take the cube root

• Multiply by 8 and take the cube root

• Multiply by 8 and square the result

• Divide by 8 and square the result

Tags

CCSS.HSA.APR.B.3

What is the result of the fourth root of 81?

• 3

• 9

• 81

• No solution

Tags

CCSS.HSN.RN.A.2