Operations with Radicals Practice

Simplify the following:

 $\sqrt{28x^4y^4}$  

•  $4x^2y^2\sqrt{7}$  

•  $2x^2y^2\sqrt{7}$  

•  $7xy\sqrt{4xy}$  

•  $2xy\sqrt{7}$  

Tags

CCSS.HSN.RN.A.2

Simplify the following:

 $3\sqrt{2x}\cdot\sqrt{2x^2}$  

•  $3\sqrt{4x^3}$  

•  $12x\sqrt{x}$  

•  $6x\sqrt{x}$  

•  $12x^3$  

Simplify the following:

 $\frac{\sqrt{4m^4}}{5\sqrt{6m}}$  

•  $\frac{2m}{5\sqrt{6m}}$  

•  $\frac{\sqrt{2m^3}}{5\sqrt{3}}$  

•  $\frac{2m^2\sqrt{6m}}{30m}$  

•  $\frac{m\sqrt{6m}}{15}$  

Simplify the following:

 $-6\sqrt{5}+2\sqrt{45}$  

•  $0$  

•  $-4\sqrt{50}$  

•  $-20\sqrt{2}$  

•  $-12\sqrt{45}$  

Tags

CCSS.HSN.RN.A.2

Simplify the following:

 $\sqrt{5}\left(\sqrt{10}-4\sqrt{12}\right)$  

•  $-3\sqrt{10}$  

•  $\sqrt{15}-4\sqrt{17}$  

•  $\sqrt{50}-4\sqrt{60}$  

•  $5\sqrt{2}-8\sqrt{15}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the following:

 $\left(-5+\sqrt{2}\right)\left(2-\sqrt{2}\right)$  

•  $-12$  

•  $-12+7\sqrt{2}$  

•  $-10+7\sqrt{2}-\sqrt{4}$  

•  $-10-\sqrt{4}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

Simplify the following:

 $-5\sqrt{80mn}$  

•  $-50mn\sqrt{8}$  

•  $-10\sqrt{20mn}$  

•  $-20\sqrt{5mn}$  

•  $-5mn\sqrt{80}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the following:

 $\sqrt{30x}\cdot-2\sqrt{5x^2}$  

•  $-10x\sqrt{6x}$  

•  $-2\sqrt{150x^3}$  

•  $5x\sqrt{6x}$  

•  $-2x\sqrt{35x}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the following:

 $\frac{4}{\sqrt{6x^2y^4}}$  

•  $\frac{4}{xy^2\sqrt{6}}$  

•  $\frac{2}{xy^2\sqrt{3}}$  

•  $\frac{2\sqrt{3}}{3xy^2}$  

•  $\frac{2\sqrt{6}}{3xy^2}$  

Simplify the following:

 $3\sqrt{54}-2\sqrt{6}+2\sqrt{3}$  

•  $3\sqrt{51}$  

•  $9\sqrt{9}$  

•  $7\sqrt{6}+2\sqrt{3}$  

•  $25\sqrt{6}+2\sqrt{3}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2