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 (3y-2)^{1/5} + 5 = 6?

Back

Subtract 5 from both sides to get (3y-2)^{1/5} = 1, then raise both sides to the power of 5 to find y = 1.

Front

What is the solution to the cube root equation x^{1/3} = 3?

Back

To solve for x, cube both sides to get x = 27.

Front

What is the solution to the cube root equation x^{1/3} = 6?

Back

To solve for x, cube both sides to get x = 216.

Front

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

Back

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

Front

What is the general form of an nth root equation?

Back

An nth root equation can be expressed as x^{1/n} = a, where a is a constant.

Front

How do you isolate the variable in an nth root equation?

Back

You can isolate the variable by raising both sides of the equation to the power of n.

Front

What is the relationship between roots and exponents?

Back

The nth root of a number is equivalent to raising that number to the power of 1/n.

Front

What is the cube root of 64?

Back

The cube root of 64 is 4, since 4^3 = 64.

Front

How do 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.