Divide Square Roots

Divide Square Roots

Divide even numbers by   $\sqrt{2}$  

 $\frac{a}{\sqrt{2}}$  where a is divisible by 2

 $\frac{4}{\sqrt{2}}$  

Divide 2 into 4, multiply what is left by  $\sqrt{2}$  

 $\frac{4}{\sqrt{2}}$  =  $2\sqrt{2}$  

Divide 2 into 4, multiply what is left by  $\sqrt{2}$  

Multiple Choice

 $\frac{8}{\sqrt{2}}$  

•  $2\sqrt{2}$  

•  $4\sqrt{2}$  

•  $8\sqrt{2}$  

Multiple Choice

 $\frac{100}{\sqrt{2}}$  

•  $50\sqrt{2}$  

•  $100\sqrt{2}$  

• 50

Multiple Choice

 $\frac{6}{\sqrt{2}}=$  

•  $6\sqrt{3}$  

•  $3\sqrt{2}$  

•  $3$  

 $\frac{3}{\sqrt{2}}=\ 1.5\sqrt{2}\ \ or\ \ \frac{3\sqrt{2}}{2}$  

Multiple Choice

 $\frac{7}{\sqrt{2}}$  

• 3

• 3.5

•  $3.5\sqrt{2}$  

Multiple Choice

 $\frac{11}{\sqrt{2}}$  

•  $5.5\sqrt{2}$  

•  $5\sqrt{2}$  

Dividing when there is a radical in the numerator and denominator

 $\frac{\sqrt{2}}{\sqrt{2}}\ =\ 1$  

Multiple Choice

 $\frac{3\sqrt{2}}{\sqrt{2}}$  

•  $3$  

•  $1.5\sqrt{2}$  

•  $1.5\sqrt{4}$  

Multiple Choice

 $\frac{75\sqrt{2}}{\sqrt{2}}$  

•  $75\sqrt{4}$  

•  $37.5\sqrt{4}$  

•  $75$  

 $\frac{\sqrt{6}}{\sqrt{2}}\ =\ \sqrt{3}$  

IF possible, divide the radicand in the numerator by the radicand in the denominator to simplify.

Multiple Choice

 $\frac{\sqrt{14}}{\sqrt{2}}\ =\$  

•  $\sqrt{7}$  

•  $7$  

•  $2\sqrt{7}$  

Multiple Choice

 $\frac{\sqrt{12}}{\sqrt{2}}=$  

•  $\sqrt{6}$  

•  $2\sqrt{6}$  

Multiple Choice

 $\frac{2\sqrt{12}}{\sqrt{2}}=$  

•  $2\sqrt{6}$  

•  $\sqrt{12}$  

•  $\sqrt{6}$  

Multiple Choice

 $\frac{8\sqrt{6}}{2\sqrt{2}}=$  

•  $2\sqrt{6}$  

•  $4\sqrt{3}$  

•  $4\sqrt{2}$  

Hardest case: radicand in numerator is NOT divisible by the radicand in the denominator

 $\frac{2\sqrt{3}}{\sqrt{2}}=\ \sqrt{6}$  

 $\sqrt{2}\ doesn't\ go\ into\ \sqrt{3},\ 2\ \div\ 2\ =\ 1\ \ \cdot\ \sqrt{3}\sqrt{2}=\sqrt{6}$  

 $\frac{4\sqrt{3}}{\sqrt{2}}=2\sqrt{6}$  

 $\frac{10\sqrt{5}}{\sqrt{2}}=5\sqrt{10}$  

Multiple Choice

 $\frac{12\sqrt{7}}{\sqrt{2}}=$  

•  $12\sqrt{14}$  

•  $2\sqrt{14}$  

•  $6\sqrt{14}$  

Multiple Choice

 $\frac{12\sqrt{3}}{\sqrt{2}}=$  

•  $6\sqrt{6}$  

•  $2\sqrt{6}$  

•  $12\sqrt{6}$  

Multiple Choice

 $\frac{9\sqrt{3}}{\sqrt{2}}=$  

•  $9\sqrt{6}$  

•  $2.5\sqrt{6}$  

•  $4.5\sqrt{6}$  

Multiple Choice

 $\frac{9\sqrt{5}}{\sqrt{2}}=$  

•  $4.5\sqrt{10}$  

•  $9\sqrt{10}$  

•  $4.5\sqrt{5}$