Solving Nth Root Equations

Front

What is the definition of an nth root?

Back

The nth root of a number x is a number r such that r^n = x. For example, the cube root of 27 is 3, since 3^3 = 27.

Front

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

Back

To solve for x, first isolate the square root: (x + 2)^(1/2) = 3. Then square both sides: x + 2 = 9, so x = 7.

Front

What is the cube root of 64?

Back

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

Front

How do you simplify (2^6)?

Back

2^6 = 64.

Front

What is the solution to the equation x^3 = 984?

Back

The solution is x = 984^(1/3) = 9.97 (approximately).

Front

What is the definition of a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root or cube root.

Front

How do you solve the equation x^3 = 228?

Back

To solve for x, take the cube root: x = 228^(1/3) = 6.02 (approximately).

Front

What is the value of n if n^2 = 625?

Back

n = 25 or n = -25.

Front

What is the principle of squaring both sides of an equation?

Back

Squaring both sides of an equation is a method used to eliminate square roots, but it can introduce extraneous solutions.

Front

How do you express the cube root of a product?

Back

The cube root of a product can be expressed as the product of the cube roots: ∛(a*b) = ∛a * ∛b.