Solving Equations with Roots

The video tutorial teaches how to solve equations using nth roots, focusing on the differences between even and odd exponents. It covers solving equations with both types of exponents, including handling complex equations with parentheses and fractional equations. The tutorial also explains how to find approximate solutions using a calculator for non-integer results.

What is the first step in solving an equation using nth roots?

• Multiply both sides by the exponent

• Subtract the constant term

• Identify the coefficient

• Identify the exponent as even or odd

If an equation has an even exponent, how many solutions should you expect?

• Three solutions

• No solutions

• Two solutions

• One solution

What is the cube root of 216?

• 6

• 4

• 5

• 7

In the equation 5x^3 = 1080, what is the value of x?

• 6

• 4

• 7

• 5

What is the first step in solving x^6 + 36 = 100?

• Add 36 to both sides

• Subtract 36 from both sides

• Multiply both sides by 6

• Divide both sides by 6

What is the sixth root of 64?

• 5

• 4

• 3

• 2

What are the solutions for x in the equation x^6 + 36 = 100?

• x = 5 and x = -5

• x = 2 and x = -2

• x = 3 and x = -3

• x = 4 and x = -4

What is the fourth root of 256?

• 5

• 4

• 3

• 2

In the equation (x - 5)^4 = 256, what are the possible values of x?

• x = 9 and x = 1

• x = 6 and x = 4

• x = 7 and x = 3

• x = 8 and x = 2

What is the first step in solving (x + 10)^5 = 70?

• Multiply both sides by 5

• Take the fifth root of both sides

• Subtract 10 from both sides

• Add 10 to both sides