Solving Equations with Square Root

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number.

Front

Solve for x: 5x² = 500

Back

x = ±10

Front

What does it mean to solve an equation by taking the square root?

Back

It means isolating the variable and applying the square root to both sides of the equation.

Front

Solve for x: 7x² + 1 = 8

Back

x = ±1

Front

What is the solution type for the equation 3x - 7 = 3(x - 3) + 2?

Back

Infinite solutions.

Front

Solve for x: x² - 4 = 77

Back

x = ±9

Front

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

Back

It allows us to eliminate the square root by raising both sides to the power of 2.

Front

Solve for a: 10 - 3a² = -2

Back

a = ±2.

Front

What is the discriminant in a quadratic equation?

Back

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

Front

How do you determine if an equation has no real solutions?

Back

If the discriminant is less than zero, the equation has no real solutions.