Solving Radical Inequalities

The video tutorial explains how to solve radical inequalities, focusing on both square and cube roots. It emphasizes the importance of ensuring the values under even roots remain non-negative and highlights the need to flip inequality symbols when multiplying or dividing by negative numbers. The tutorial provides step-by-step examples, including handling compound inequalities, and concludes with a summary of key points.

What is the key consideration when solving radical inequalities?

• Ignoring the root entirely

• Always flipping the inequality sign

• Considering the values under the root

• Ensuring the variable is always positive

Why can't we have negative numbers under a square root in inequalities?

• Because it makes the inequality unsolvable

• Because it results in imaginary numbers

• Because it makes the solution set infinite

• Because it flips the inequality sign

What is the first step in solving the inequality 2√x ≥ 8?

• Subtract 5 from both sides

• Divide both sides by 2

• Square both sides

• Add 5 to both sides

After isolating the square root in the inequality 2√x ≥ 8, what is the next step?

• Add 2 to both sides

• Divide both sides by 2

• Square both sides

• Subtract 2 from both sides

What is the solution to the inequality √x ≥ 4?

• x ≥ 16

• x ≤ 16

• x ≤ 4

• x ≥ 4

When solving cube root inequalities, why don't we worry about negative values under the root?

• Because cube roots are always positive

• Because cube roots can handle negative numbers

• Because cube roots of negative numbers are positive

• Because cube roots of negative numbers are undefined

What is the first step in solving the inequality 4∛(x+1) ≤ 24?

• Add 4 to both sides

• Subtract 4 from both sides

• Divide both sides by 4

• Multiply both sides by 4

After isolating the cube root in the inequality 4∛(x+1) ≤ 24, what is the next step?

• Subtract 1 from both sides

• Add 1 to both sides

• Square both sides

• Cube both sides

What is the solution to the inequality ∛(x+1) ≤ 6?

• x ≥ 215

• x ≤ 215

• x ≤ 216

• x ≥ 216

In the inequality 3√(x-2) ≤ 15, what is the first step to isolate the square root?

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

• Subtract 3 from both sides