Operations with Radicals

Master operations with radicals! Simplify expressions, classify numbers, and solve geometry problems involving radicals.

1. Which of the following radical expression is equivalent to √45 - 4√5 0 -√5 √5 -3√5 2. Which of the following operations results in a rational number? √49 + 0.8 √8.√3 π + 2 (-3)(-√7) 3. Which of the following radical expressions is equivalent to (4√6)(√2) in its simplest form? 4√12 6√3 2√3 8√3 4. Given the radical above what is its quotient in simplest form? 5. If the length of a rectangle is √8 + 2 and the width is √5, what is the perimeter of the rectangle in simplest form? Hint - sketch a rectangle with the measurements. 2√8 + 2√5 + 4 4√2 + 2√5 + 4 4√13 + 4 6√7 + 4 6. What is the perimeter of the rectangle shown in its simplest form? 28√3 10√35 2√12 + 8√27 5√3 7. Find the area of the rectangle show in its simplest form. 2√12 + 2√3 + 8 8√3 + 8 4√12 + √36 2√3 + 6 8. Consider the isosceles triangle below, is the side length √3 + 2 rational or irrational? Explain your reasoning. 9. The expression 2(√3 +2) +√5 can be used to find the perimeter of the triangle, what does the "2" represent in this expression? 10. What is the perimeter of the triangle? 2√2 + √5 + 3 √9 + 3 √7 + 3 √4 + √5 + 3