Simplifying Radicals for AP Precalculus

Judy from the AP program introduces Lesson 12 on radical expressions, a crucial topic for AP pre-calculus. The lesson covers basic concepts, evaluating square and cube roots, solving right triangles using the Pythagorean theorem, and simplifying radical expressions. Students are encouraged to practice and seek help if needed. The lesson aims to build a solid foundation for more complex topics in AP pre-calculus.

What should you do if you find the content of the lesson unfamiliar?

• Ask a friend to do the problems for you.

• Ignore the unfamiliar content.

• Take advantage of the problem set and check your answers.

• Skip the lesson and move on to the next one.

What is the term for the number that falls underneath the root sign in a radical expression?

• Exponent

• Radicand

• Radical

• Index

What is the cube root of 125?

• 5

• 4

• 6

• 3

If the square root of 90 falls between 9 and 10, what is its approximate value?

• 9.5

• 8.5

• 10.5

• 11.5

In the Pythagorean theorem, what does 'c' represent?

• One of the legs of the triangle

• The hypotenuse

• The area of the triangle

• The perimeter of the triangle

What must be done before simplifying a radical expression that includes addition under one radical sign?

• Add the terms together

• Multiply the terms

• Divide the terms

• Subtract the terms

What is the simplified form of the square root of 300?

• 20√1.5

• 5√6

• 15√2

• 10√3

How do you rationalize the denominator of a fraction with a radical in the denominator?

• Multiply the numerator and denominator by the same radical

• Add the same radical to the numerator

• Divide the numerator by the same radical

• Subtract the same radical from the denominator

What is the simplified form of 2√3 over 3√10?

• 2√3/10

• √3/10

• 2√30/30

• √30/15

What is the final simplified form of the expression 2√3 + 5√12?

• 15√3

• 10√3

• 7√3

• 12√3