3.11 Exit Ticket

The number under the radical sign or square root sign  is called the ______.

• radical sign
• radicand
• factor
• exponent

√125 =

• 5√5

• 25√5

• 5√25

• 5√2

Answer explanation

$\sqrt{125}=\ \sqrt{25\cdot5}=\sqrt{25}\cdot\ \sqrt{5}=\$
$\sqrt{5^2}\cdot\sqrt{5}=5\cdot\sqrt{5}=5\sqrt{5}$

125 is the radicand. Factor the radicand and choose the factor pair with the largest square root.

4√3 - √12

• √6

• 2√3

• √2

• √5

Answer explanation

$4\sqrt{3}\ -\ \sqrt{12}\ =\ 4\sqrt{3}\ -\ \sqrt{4\cdot3}$ $=4\sqrt{3}\ -\sqrt{4}\cdot\sqrt{3}\ =\ 4\sqrt{3}\ -\sqrt{2^2}\cdot\sqrt{3}$ $=\ 4\sqrt{3}\ -2\sqrt{3}\ =\ 2\sqrt{3}$


The 4√3 is already simplified. Simplify the √12. 4 and 3 are factors of 12. Rewrite √12 in terms of its factors. √4√3 simplifies to 2√3. Subtract 2√3 from 4√3 to get 2√3.

Simplify: 

 $\sqrt{a^3}$  

• a√a

• a

•  $a^2$  

• already simplified

Answer explanation

Simplify the radicand by finding multiples of  $a^2$  : $a^3\ =\ a^2\ \cdot\ a$  . Therefore  $\sqrt{a^3}=\ \sqrt{a^2\cdot a}\ =\ \sqrt{a^2}\sqrt{a}=a\sqrt{a}$  

√5 × √10

• 50

• 2√5

• 5√2

• 5√10

Answer explanation

Multiply radicands together

√5 × √10 = √50

Simplify by factoring out the perfect square

√50 = √25*2 = √25*√2 = 5√2