Solving Nth Root Equations

Front

What is the first step to eliminate an nth root from an equation?

Back

You need to bring both sides of the equation to the power of n.

Front

How do you solve the equation x = ∛27?

Back

x = 3, since 3^3 = 27.

Front

What is the solution to the equation (3y - 2)^{1/5} + 5 = 6?

Back

y = 1.

Front

What does taking the nth root of an expression mean mathematically?

Back

It is the same as raising the expression to the power of 1/n.

Front

How do you solve the equation x = ∛228?

Back

x = 6, since 6^3 = 216 and 7^3 = 343, so x is approximately 6.

Front

What is the general form of an nth root equation?

Back

x = n√a, where a is the number and n is the degree of the root.

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inverse operations; taking the nth root is the same as raising to the power of 1/n.

Front

How can you check if your solution to an nth root equation is correct?

Back

Substitute the solution back into the original equation to verify if both sides are equal.

Front

What is the cube root of a negative number?

Back

The cube root of a negative number is also negative, e.g., ∛(-27) = -3.

Front

What is the domain of the function f(x) = ∛x?

Back

The domain is all real numbers, since you can take the cube root of any real number.