Adding, Subtracting, Multiplying, and Dividing Radicals

Adding, Subtracting, Multiplying, and Dividing Radicals

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Multiple Choice

Simplify

 $3^{\ \ 3}\sqrt{54}-2^{\ \ 3}\sqrt{2}+7^{\ \ 3}\sqrt{-16}$  

•  $-7^{\ \ 3}\sqrt{2}$  

•  $3^{\ \ 3}\sqrt{2}-2^{\ \ 3}\sqrt{2}-14$  

•  $9^{\ \ 3}\sqrt{2}-2^{\ \ 3}\sqrt{2}-14^{\ \ 3}\sqrt{2}$  

Multiple Choice

Simplify  $10\sqrt{28}-^3\sqrt{-56}-4\sqrt{175}$  

•  $-2\sqrt{7}$  

•  $-2^{\ \ 3}\sqrt{7}$  

•  $-22^{\ \ 3}\sqrt{7}$  

Multiple Choice

Simplify  $^{\ \ 3}\sqrt{-40a^7}+2a^2\times^3\sqrt{135a^4}$  

•  $-2a^{2\ \ 3}\sqrt{5a}+6a^{3\ \ 3}\sqrt{5a}$  

•  $4a^{3\ \ 3}\sqrt{5a}$  

•  $4a^{\ \ 3}\sqrt{5a}$  

Multiple Choice

Simplify completely.

 $3\sqrt{10}\times-2\sqrt{18}$  

• Cannot be simplified further

•  $-6\sqrt{180}$  

•  $-36\sqrt{5}$  

•  $6\sqrt{180}$  

Multiple Choice

Simplify completely. 
 $-3^{\ \ 4}\sqrt{64}\times-^4\sqrt{8}$  

•  $12^{\ \ 4}\sqrt{4}$  

•  $-6^{\ \ 4}\sqrt{2}$  

•  $12^{\ \ 4}\sqrt{2}$  

•  $-12^{\ \ 4}\sqrt{2}$  

Multiple Choice

 $\sqrt{6x^4}\times5\sqrt{8x^5}$  

•  $5\sqrt{48x^9}$  

•  $5\sqrt{48x^{20}}$  

•  $20x^4\sqrt{3x}$  

Multiple Choice

 $2^{\ \ 4}\sqrt{p^2q}\times7^{\ \ 4}\sqrt{p^3q^{10}}$  

•  $14pq^{2\ \ 4}\sqrt{pq^3}$  

•  $14^{\ \ 4}\sqrt{p^5q^{11}}$  

•  $14pq^{2\ \ }\sqrt{pq^3}$  

Multiple Choice

Simplify completely.

 $\left(8-\sqrt{10}\right)\left(3-\sqrt{10}\right)$  

•  $34-11\sqrt{10}$  

•  $24-11\sqrt{10}+\sqrt{100}$  

•  $24-11\sqrt{10}+10$  

Multiple Choice

Simplify completely.

 $\left(4-\sqrt{5}\right)^2$  

•  $16-8\sqrt{5}$  

•  $21$  

•  $21-8\sqrt{5}$  

Multiple Choice

Simplify completely.

 $\left(\sqrt{x}-\sqrt{8}\right)\left(\sqrt{x}+\sqrt{2}\right)$  

•  $x-6\sqrt{x}-4$  

•  $x-6\sqrt{x}+4$  

Multiple Choice

 $Simplify\ \frac{28^{\ \ 3}\sqrt{-16m^6}}{4^{3\ \ }\sqrt{2m}}$  

•  $7^{\ \ 3}\sqrt{-8m^5}$  

•  $-14m^{\ \ 3}\sqrt{m^2}$  

•  $-14^{\ \ 3}\sqrt{m^5}$  

Multiple Choice

 $Simplify\ ^4\sqrt{\frac{32w}{81}}$  

•  $6w^{\ \ 4}\sqrt{2}$  

•  $\frac{2^{\ \ 4}\sqrt{2w}}{3}$  

•  $\frac{2w^{\ \ 4}\sqrt{2}}{3}$  

•  $\frac{2^{\ \ 4}\sqrt{w}}{3}$  

Multiple Choice

 $Simplify\ \frac{\sqrt{8}-\sqrt{2}}{\sqrt{2}}$  

•  $1$  

•  $\sqrt{4}-1$  

•  $\sqrt{16}-\sqrt{4}$  

• 2

Multiple Choice

 $Simplify\ \frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}}$  

•  $\frac{\sqrt{8}}{2}$  

•  $\frac{\sqrt{6}+\sqrt{2}}{2}$  

•  $\sqrt{4}$  

Multiple Choice

 $Simplify\ \frac{8-\sqrt{6}}{3-4\sqrt{6}}$  

•  $\frac{24+29\sqrt{6}}{-87}$  

•  $\frac{29\sqrt{6}}{-87}$  

•  $3+4\sqrt{6}$