To recognize and create equivalent radical expressions To square binomials with radical terms To use the distributive property with radicals To simplify expressions under a radical by factoring out a perfect square To revisit quadratic equations and parabolas

Draw a segment that is units long.

Radical Expressions How can you tell if two different radical expressions are equivalent? Is it possible to add, subtract, multiply, or divide radical expressions? You’ll answer these questions as you work through this investigation. On graph paper, draw line segments for each length given below. You may need more than one triangle to create some of the lengths.

Do any of the segments seem to be the same length? If so, which ones? Use your calculator to find a decimal approximation to the nearest ten thousandth for each expression in Step 1.Which expressions are equivalent?

Make a conjecture about another way to write each expression at the right. Choose positive values for the variables, and use your calculator to test whether your expression is equivalent to the original expression. Summarize what you’ve discovered about adding, multiplying, and dividing radical expressions.

Use what you’ve learned to find the area of each rectangle below. Give each answer in radical form as well as a decimal approximation to the nearest hundredth. hundredth.

Example B Rewrite this expression with as few square root symbols as possible and no parentheses. Use your calculator to check your answer.

Example C Rewrite each expression with as few square root symbols as possible and no parentheses.