CPM Homework Help : PCT Problem 4-42

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4-42.

Simplify each expression.

$5 \sqrt { 2 } + 3 \sqrt { 7 } - 2 \sqrt { 2 } + 4 \sqrt { 7 }$
Hint (a):
Combine the $\sqrt{2}$ ’s with the $\sqrt{2}$ s and with the $\sqrt{7}$ s.
Answer (a):
$3\sqrt{2}+7\sqrt{7}$

$4 ( \sqrt [ 3 ] { 2 } ) + 5 \sqrt { 2 } - 7 \sqrt [ 3 ] { 2 } + \sqrt { 2 }$
Hint (b):
$\sqrt[3]{2}$ is different from $\sqrt{2}$

$\sqrt { 20 } + \sqrt { 45 }$
Hint (c):
Rewrite each term in simple radical form so that you can identify like terms.
Steps (c):
$\sqrt{(4)(5)}+\sqrt{(9)(5)}$

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

$3 \sqrt { 12 } - \sqrt { 32 } + \sqrt { 27 } + 2 \sqrt { 8 }$
Step (d):
$3\sqrt{4}\sqrt{3}-\sqrt{16}\sqrt{2}+\sqrt{9}\sqrt{3}+2\sqrt{4}\sqrt{2}$

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