Chapter 6.4, Problem 51PE

For Exercise 35-64, add or subtract the radical expressions as indicated. (See Example 3-4.)

51. $5p\sqrt{20p^2}+p^2\sqrt{80}$

Example 3

Adding and Subtracting Radicals

Simplify the radicals and add or subtract as indicated. Assume all variables represent positive real numbers.

a. $3\sqrt{8}+\sqrt{2}$

b. $8\sqrt{x^3{y}^2}-3y\sqrt{x^3}$

c. $\sqrt{50x^2{y}^5}-13\sqrt{2x^2{y}^3}+xy\sqrt{98y^3}$

Example 4

Adding Radicals Expressions

Add the radicals. Assume that $x\ge 0.3\sqrt{2x^2}+\sqrt{8}$