Simplify Radicals

Simplify the following radical expression:  $\sqrt{242}$  

• 2 $\sqrt{11}$  

• 2 $\sqrt{22}$  

• 11 $\sqrt{2}$  

• 9 $\sqrt{7}$  

Tags

CCSS.HSN.RN.A.2

Simplify the radical expression below:  $\sqrt{80}$  

• 10 $\sqrt{8}$  

• 4 $\sqrt{5}$  

• 2 $\sqrt{20}$  

• 4 $\sqrt{20}$  

Tags

CCSS.HSN.RN.A.2

Which of the following shows a radical expression that has been correctly simplified?

• $\sqrt{72x^3}$ = 6x $\sqrt{2x}$

• $\sqrt{24x^4}$ = 4 $x^4$ $\sqrt{6}$

• $\sqrt{54x^5}$ = 3 $x^4$ $\sqrt{6x}$

• $\sqrt{98x^6}$ = 7 $x^3$ $\sqrt{14}$

Tags

CCSS.HSN.RN.A.2

Which of the following expressions is not already in simplest form?

• $\sqrt{10xy}$

• $\sqrt{18mn}$

• $\frac{\sqrt{6ab}}{3b}$

• $\frac{\sqrt{15rt}}{5r}$

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Carlo was simplifying the expression  $\sqrt{32n^4k^7}$  on his homework.  He recorded his answer as 16 $n^2k^3\sqrt{2k}$  .  What mistake did Carlo make in simplifying?  

• Carlo did not make a mistake.

• He should have taken the square root of 16 instead of writing 16.
  

• He should have recorded the exponent on the variable k as 4 instead of 3.

• He should not have written he  $k^3$  on the outside and instead left it as  $k^7$  under the radical symbol.

Tags

CCSS.HSN.RN.A.2

Which of the following shows the correct simplification of  $\frac{\sqrt{50n^2p^5}}{5np}$  ?

•  $p^2\sqrt{10}$  

•  $\frac{5np^2\sqrt{2p}}{n}$  

•  $p\sqrt{2p}$  

•  $\frac{p^2\sqrt{10p}}{n}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify:  $4\sqrt{2}\ \times\ 5\sqrt{6}$  

•  $20\sqrt{12}$  

•  $40\sqrt{3}$  

•  $80\sqrt{3}$  

•  $18\sqrt{2}$  

Tags

CCSS.HSN.RN.A.2

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

•  $4\sqrt{3}$  

•  $4\sqrt{6}$  

•  $3\sqrt{6}$  

•  $3\sqrt{3}$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Simplify:  $\frac{8\sqrt{3}}{10\sqrt{6}}$  

•  $\frac{4\sqrt{2}}{5}$  

•  $\frac{4\sqrt{18}}{30}$  

•  $\frac{4}{5\sqrt{2}}$  

•  $\frac{2\sqrt{2}}{5}$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Simplify:  $\left(4\sqrt{2}\ -\ \sqrt{2}\right)\ \left(3\sqrt{3\ }\ +\ \sqrt{5}\right)$  

•  $15\sqrt{6}\ +\ 5\sqrt{10}$  

•  $-24\sqrt{15}$  

•  $5\sqrt{2}+3\sqrt{3}+\sqrt{5}$  

•  $9\sqrt{6}+3\sqrt{10}$  

Tags

CCSS.HSN.RN.A.2