solving with square roots (short flashcard)

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

What does it mean to solve an equation using square roots?

Back

Solving an equation using square roots involves isolating the variable and taking the square root of both sides of the equation.

Front

What is the principle of squaring a binomial?

Back

The principle of squaring a binomial states that (a + b)² = a² + 2ab + b².

Front

What is the first step in solving (2x - 1)² = 49?

Back

The first step is to take the square root of both sides of the equation.

Front

What are the two solutions to the equation (2x - 1)² = 49?

Back

The two solutions are x = 4 and x = -3.

Front

How do you isolate the variable in the equation (2x - 1)² = 49?

Back

You first take the square root of both sides, then solve for x by adding 1 and dividing by 2.

Front

What is the square root of 49?

Back

The square root of 49 is 7.

Front

What does it mean if an equation has two solutions?

Back

It means that there are two different values for the variable that satisfy the equation.

Front

How do you check if your solutions are correct?

Back

You can substitute the solutions back into the original equation to see if both sides are equal.

Front

What is the difference between a perfect square and a non-perfect square?

Back

A perfect square is a number that has an integer as its square root, while a non-perfect square does not.