Simplifying Radicals with Variables in Algebra 1

The video tutorial covers simplifying radicals, including those with variables. The teacher explains how to break down radicals into products of numbers, focusing on finding the largest perfect square. The lesson progresses to handling variables within radicals, identifying patterns in exponents, and dealing with odd exponents. Practice problems are provided for students to apply the concepts. The teacher concludes with encouragement and a reminder to review the material.

What is the goal when simplifying a radical that is not a perfect square?

• To break it into a sum of numbers

• To break it into a product of numbers, one being the largest perfect square

• To convert it into a fraction

• To multiply it by itself

What is the simplified form of √27?

• √9 + √3

• 3√3

• 9√3

• 27√3

What happens to x² when you take the square root of it?

• It becomes x²

• It becomes x

• It becomes 2x

• It remains the same

How do you simplify √18x²?

• 2x√9

• 3x√2

• 9x√2

• 6x√3

What is the simplified form of √x⁶?

• x

• x⁶

• x²

• x³

How do you simplify √x⁸?

• x

• x⁸

• x²

• x⁴

What is the simplified form of √x¹⁶?

• x⁸

• x⁴

• x²

• x

How do you simplify √24x¹⁰y⁶?

• 2x⁵y³√6

• 4x⁵y³√6

• 2x¹⁰y⁶√24

• 6x⁵y³√4

What do you do with odd exponents when simplifying radicals?

• Convert them to even exponents

• Multiply them by 2

• Ignore them

• Split them into an even exponent and one left over

What is the simplified form of √x¹³y⁶?

• x⁶y³

• x⁶y⁶

• x⁷y³

• x⁶y³√x