Solving Equations Using Square and Cube Roots

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is the solution to the equation x² - 49 = 0?

Back

x = 7 or x = -7.

Front

What does it mean if a quadratic equation has no real solutions?

Back

A quadratic equation has no real solutions if the expression under the square root (the discriminant) is negative, indicating that the solutions are complex numbers.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots.

Front

How do you solve the equation x² + 12 = 5?

Back

Rearranging gives x² = -7, which has no real solutions since the square root of a negative number is not real.

Front

What is a cube root?

Back

The cube root of a number x is a value y such that y³ = x. For example, the cube root of 27 is 3, since 3³ = 27.

Front

How do you solve a cubic equation like x³ - 25 = 100?

Back

First, rearrange to x³ = 125, then take the cube root of both sides to find x = 5.

Front

What is the solution to the equation 5b² - 4 = 41?

Back

b = 3 or b = -3.