Solving Square Root Equations

Front

What is a square root equation?

Back

A square root equation is an equation that contains a variable within a square root. It can often be solved by isolating the square root and then squaring both sides of the equation.

Front

How do you isolate a square root in an equation?

Back

To isolate a square root, you need to move all other terms to the opposite side of the equation. For example, in @@ ext{if } \\sqrt{x-7} = 6, ext{ you would add 7 to both sides to isolate the square root.}$$

Front

What is the first step in solving @@ ext{if } \\sqrt{x-7} = 6?$$

Back

The first step is to square both sides of the equation to eliminate the square root: @@x - 7 = 36$$.

Front

What is the solution to @@ ext{if } \\sqrt{x-7} = 6?$$

Back

The solution is @@x = 43$$.

Front

How do you check the solution of a square root equation?

Back

To check the solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is the domain of a square root function?

Back

The domain of a square root function is the set of all real numbers for which the expression inside the square root is non-negative.

Front

What does it mean to have no solution in a square root equation?

Back

No solution occurs when the equation leads to a contradiction, such as a negative number under the square root.

Front

Solve for x: @@ ext{if } \\sqrt{x+29} - 13 = -8$$

Back

The solution is @@x = -4$$.

Front

What is the solution to @@ ext{if } \\sqrt{x+80} - 9 = 0?$$

Back

The solution is @@x = 1$$.

Front

Back

The transformation is a horizontal shift to the right by 4 units.