Solving Quadratics by Square Roots

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 of the form x² = a, take the square root of both sides, resulting in x = ±√a.

Front

What is the solution to the equation k² - 6 = 43?

Back

k = 7, k = -7.

Front

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

Back

It means that the equation does not intersect the x-axis, and the solutions are complex numbers.

Front

Solve for a: a² + 9 = 9.

Back

a = 0.

Front

What is the solution to the equation (h - 2)² = 9?

Back

h = 5, h = -1.

Front

How do you isolate a variable in a quadratic equation?

Back

To isolate a variable, rearrange the equation to one side, set it equal to zero, and then apply the square root method if applicable.

Front

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

Back

b = 3, b = -3.

Front

What is the first step in solving (x - 7)² + 4 = 40?

Back

Subtract 4 from both sides to get (x - 7)² = 36.

Front

What is the square of a negative number?

Back

The square of a negative number is positive. For example, (-3)² = 9.