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.

Tags

CCSS.8.EE.A.2

Front

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

Back

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

Tags

CCSS.8.EE.A.2

Front

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

Back

x = ±1.

Tags

CCSS.8.EE.A.2

Front

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

Back

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

Tags

CCSS.8.EE.A.2

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.

Tags

CCSS.8.EE.A.2

Front

What are the solutions to the equation x² = 100?

Back

x = 10 or x = -10.

Tags

CCSS.8.EE.A.2

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the ± symbol in solutions?

Back

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

Tags

CCSS.8.EE.A.2