Understanding Radical Equations

The video tutorial explains how to solve equations containing radicals by isolating the radical on one side, raising both sides to the power of the index to eliminate the radical, and solving the resulting equation. Two examples are provided: the first involves a simple radical equation, while the second is more complex, requiring additional steps to isolate the radical. Each solution is verified by substituting back into the original equation. The video concludes with a preview of the next topic, which involves solving radical equations with variables both inside and outside the radical.

What is the first step in solving an equation with one radical?

• Divide both sides by the radical

• Add a constant to both sides

• Isolate the radical on one side

• Multiply both sides by the index

In the first example, what operation is used to eliminate the +3?

• Adding 3 to both sides

• Multiplying both sides by 3

• Subtracting 3 from both sides

• Dividing both sides by 3

What is the solution for x in the first example after solving the equation?

• x = 5/17

• x = 17/5

• x = 5

• x = 17

How do you verify the solution in the first example?

• By substituting the solution back into the original equation

• By checking if both sides are equal after squaring

• By solving a different equation

• By graphing the equation

In the second example, what is the first step to isolate the square root?

• Divide both sides by 3

• Multiply both sides by -3

• Add 2 to both sides

• Subtract 2 from both sides

What is the result of dividing both sides by -3 in the second example?

• The square root of x + 3 equals 5/3

• The square root of x + 3 equals -5/3

• The square root of x + 3 equals -3/5

• The square root of x + 3 equals 3/5

What is the final solution for x in the second example?

• x = 2/9

• x = -2/9

• x = 9/2

• x = -9/2

How is the common denominator found when solving 25/9 - 3?

• By multiplying by 3/3

• By adding 9 to the numerator

• By subtracting 9 from the denominator

• By multiplying by 9/9

What is the square root of 25/9?

• 9/5

• 5/3

• 3/5

• 5/9

What is the purpose of the next video as mentioned in the conclusion?

• To solve linear equations

• To solve equations with x inside and outside the square root

• To solve quadratic equations

• To solve equations with multiple radicals