Radicals Review

Find a simplified expression for the perimeter of this shape

• $44\sqrt{5}-8\sqrt{6}-32$

• $22\sqrt{5}-4\sqrt{6}-16$

• $12\sqrt{2}+4\sqrt{3}+4$

• $4\sqrt{6}+\sqrt{3}-8-\sqrt{2}$

What does the expression $7\sqrt{7}-6\sqrt{12}-\left(4\sqrt{28}+4\sqrt{3}\right)$ simplify to? 

•  $15\sqrt{7}-16\sqrt{3}$  

•  $15\sqrt{7}+16\sqrt{3}$  

•  $-\sqrt{7}-16\sqrt{3}$  

•  $-\sqrt{7}+16\sqrt{3}$  

State the side length of a square with an area of 1573 cm² in simplified radical form

• $11\sqrt{13}$ cm

• $\frac{1573}{\sqrt{2}}$ cm

• $786.5$ cm

• $\frac{1573}{2}$ cm

Determine the value of the expression $\sqrt{x^2+y^3}$ when  $x=7$  and  $y=4$   

•  $56$  

•  $\sqrt{11}$  

•  $\sqrt{26}$  

•  $\sqrt{113}$  

Simplify $3\sqrt{175}+6\sqrt{63}$  

•  $9+\sqrt{238}$  

•  $33\sqrt{7}$  

•  $9+2\sqrt{2}$  

•  $114$  

Simplify $6\sqrt{80}-2\sqrt{20}$  

•  $4+\sqrt{2}$  

•  $4+2\sqrt{15}$  

•  $-36$  

•  $20\sqrt{5}$  

The volume, V, in cubic units, of a cylinder is given by $V=\pi r^2h$ , where r is the radius and h is the height, both in the same units. Find the exact radius of a cylinder with a height of 64 cm and a volume of  $576\pi$ cubic cm. Express your answer in simplest form. 

•  $\frac{1}{\sqrt{64}}$ cm

•  $8$  cm

•  $9$  cm

•  $3$  cm

Express $-7\sqrt{6}\left(-6\sqrt{5}-2\sqrt{6}\right)$ in simplest form 

•  $14\sqrt{6}+42\sqrt{30}$  

•  $252$  

•  $42\sqrt{30}+84$  

•  $1260+14\sqrt{6}$  

Find a simplified expression for the area of this shape

• $9\sqrt{7}+16\sqrt{2}$

• $9\sqrt{7}-16\sqrt{2}$

• $95$

• $31$

Express $\left(\sqrt{19}-\sqrt{7}\right)\left(\sqrt{19}+\sqrt{7}\right)$ in simplest form 

•  $2\sqrt{19}-19\sqrt{7}$  

•  $2\sqrt{3}$  

•  $12$  

•  $2\sqrt{19}-2\sqrt{7}$