Radical Equations and Exponents

This lesson covers solving radical equations and inequalities, focusing on equations with radicals on both sides and fractional exponents. The instructor demonstrates solving techniques, including squaring both sides, isolating radicals, and checking solutions. The lesson includes example problems to reinforce concepts and highlights the importance of understanding rational exponents and their conversion to radicals.

What is the first step in solving an equation with radicals on both sides?

• Subtract a constant from both sides

• Multiply both sides by a constant

• Square both sides

• Add a constant to both sides

When isolating a radical, what should you do after moving terms to the other side?

• Divide by the coefficient of the radical

• Add the terms back

• Multiply by the coefficient of the radical

• Subtract the terms again

How do you handle a fractional exponent in an equation?

• Raise both sides to the reciprocal of the exponent

• Multiply both sides by the exponent

• Convert it to a decimal

• Ignore the exponent

What is the result of raising a power to another power?

• Add the exponents

• Subtract the exponents

• Multiply the exponents

• Divide the exponents

When should you consider a plus or minus in your solution?

• When the root is odd

• When the root is even

• When the equation is linear

• When the exponent is a fraction

What is the solution to the equation x plus 30 to the 1/2 power equals x?

• x = 6

• x = -5

• x = 0

• x = 30

What should you do if the solution to a quadratic equation does not satisfy the original equation?

• Ignore it

• Check for calculation errors

• Use a different method

• Consider it as a valid solution

How do you solve an equation with a rational exponent of 3/4?

• Raise both sides to the 4/3 power

• Raise both sides to the 3/4 power

• Multiply both sides by 3/4

• Divide both sides by 3/4

What is the solution to the equation 2x minus 3 to the 2/3 power plus 4 equals 13?

• x = 3

• x = 0

• x = -12

• x = 15

Why is it important to check your solutions in radical equations?

• To ensure the solution is positive

• To verify the solution satisfies the original equation

• To find additional solutions

• To simplify the solution