### Home > PC > Chapter 4 > Lesson 4.1.3 > Problem4-42

4-42.

Simplify each expression.

1. $5 \sqrt { 2 } + 3 \sqrt { 7 } - 2 \sqrt { 2 } + 4 \sqrt { 7 }$

Combine the $\sqrt{2}$’s with the $\sqrt{2}$s and with the $\sqrt{7}$s.

$3\sqrt{2}+7\sqrt{7}$

1. $4 ( \sqrt [ 3 ] { 2 } ) + 5 \sqrt { 2 } - 7 \sqrt [ 3 ] { 2 } + \sqrt { 2 }$

$\sqrt[3]{2}$  is different from $\sqrt{2}$

1. $\sqrt { 20 } + \sqrt { 45 }$

Rewrite each term in simple radical form so that you can identify like terms.

$\sqrt{(4)(5)}+\sqrt{(9)(5)}$

$2\sqrt{5}+3\sqrt{5}$

1. $3 \sqrt { 12 } - \sqrt { 32 } + \sqrt { 27 } + 2 \sqrt { 8 }$

$3\sqrt{4}\sqrt{3}-\sqrt{16}\sqrt{2}+\sqrt{9}\sqrt{3}+2\sqrt{4}\sqrt{2}$