5.1 In-Class Practice: Nth Roots

Front

What is an nth root?

Back

An nth root of a number 'a' is a number 'b' such that b^n = a. It is denoted as √[n]{a}.

Front

How do you simplify the expression 8^(1/3)?

Back

8^(1/3) simplifies to 2, since 2^3 = 8.

Front

What is the value of 27^(1/3)?

Back

27^(1/3) equals 3, because 3^3 = 27.

Front

Calculate the cube root of 125.

Back

The cube root of 125 is 5, since 5^3 = 125.

Front

What does the expression 4^(5/2) represent?

Back

4^(5/2) can be interpreted as (4^(1/2))^5, which equals 2^5 = 32.

Front

How do you solve the equation (x-2)^(1/3) - 3 = -5?

Back

To solve for x, first add 3 to both sides to get (x-2)^(1/3) = -2. Then cube both sides to find x-2 = -8, leading to x = -6.

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related; taking the nth root of a number is the same as raising that number to the power of 1/n.

Front

What is the value of 64^(1/2)?

Back

64^(1/2) equals 8, since 8^2 = 64.

Front

How do you express the square root of a number in exponential form?

Back

The square root of a number 'a' can be expressed as a^(1/2).

Front

What is the cube root of a negative number?

Back

The cube root of a negative number is also negative. For example, ∛(-8) = -2.