Solving Equations with Square Root

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. It can be positive or negative.

Front

How do you isolate x in the equation x² = a?

Back

To isolate x, take the square root of both sides: x = ±√a.

Front

What is the solution to the equation 7x² + 1 = 8?

Back

x = ±1.

Front

What is the first step to solve the equation 10 - 3a² = -2?

Back

Subtract 10 from both sides: -3a² = -12.

Front

What do you do after isolating a² in the equation 5x² = 500?

Back

Divide both sides by 5 to get x² = 100, then take the square root.

Front

What are the solutions to the equation x² = 100?

Back

x = 10 or x = -10.

Front

What does it mean if an equation has no real solutions?

Back

It means that the equation cannot be satisfied by any real number.

Front

How do you solve the equation -7x² + 21 = 84?

Back

First, isolate x²: -7x² = 63, then x² = -9, which has no real solutions.

Front

What is the process to solve quadratic equations using square roots?

Back

1. Isolate the x² term. 2. Take the square root of both sides. 3. Solve for x.

Front

What is the significance of the ± symbol in solutions?

Back

It indicates that there are two possible solutions: one positive and one negative.