Solving Radical Equations in Algebra 1

What is the first step in solving a radical equation involving a square root?

• Divide both sides by the coefficient of the radical

• Isolate the radical on one side

• Square both sides immediately

• Add the same number to both sides

What happens when you square both sides of an equation containing a square root?

• The equation becomes unsolvable

• The equation simplifies to a linear equation

• The square root is eliminated

• The variables are automatically isolated

In the equation 'sqrt(x + 5) = 13', what is the value of x after solving?

• 8

• 18

• 13

• 64

What is an extraneous solution in the context of radical equations?

• A solution that simplifies the equation

• A solution derived from incorrect operations

• A valid solution that satisfies the original equation

• A solution that does not satisfy the original equation

How can you identify an extraneous solution?

• By squaring both sides again

• By checking if the solution is a whole number

• By adding the solutions together

• By substituting back into the original equation

What is the correct solution for the equation 'x = sqrt(x + 6)'?

• x = 6

• x = 0

• x = -2

• x = 3

What mathematical operation is used to isolate the variable in a radical equation involving a cube root?

• Taking the logarithm of both sides

• Cubing both sides

• Dividing both sides by the cube root

• Multiplying both sides by three

What is the result of solving the equation '13 + sqrt(5n) = 3' for n?

• n = 20

• n = -20

• No solution

• n = 5

In the context of pendulum periods, what does the formula 'P = 2π * sqrt(L / 32)' represent?

• The acceleration due to gravity

• The period of the pendulum in seconds

• The frequency of the pendulum swings

• The length of the pendulum

If a pendulum's period is 4 seconds, is it twice as long as one with a period of 2 seconds?

• Yes, it is twice as long

• No, it is four times as long

• No, it is the same length

• Yes, it is eight times as long