Simplify Surds and Rationalise denominator

A surd is...

• A root of a number that can be simplified to a rational number.

• A root of a number that cannot be simplified to a irrational number.

• A root of a number that cannot be simplified to a rational number.

• A square root that cannot be simplified to an irrational number.

Which of the following is a surd?

•  $\sqrt{289}$  

•  $2\sqrt{4}$  

•  $\sqrt{82}$  

•  $\sqrt{25}$  

Which of the following is/are not a surd?

•  $\sqrt{144}$  

•  $\sqrt{16}$  

•  $\sqrt{5}\sqrt{11}$  

•  $\sqrt{121}\sqrt{4}$  

Which option describe the rules of surd?

• $𝑎\sqrt{x}+𝑏\sqrt{x}=(𝑎+𝑏)\sqrt{x}\$

• $\sqrt{a}-\sqrt{b}=\sqrt{a}+\sqrt{b}$

• $\sqrt{a}×\sqrt{b}=\sqrt{ab\ }\ \$

• $𝑎\sqrt{x}-𝑏\sqrt{x}=(𝑎-𝑏)\sqrt{x}$

• $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$

 $\sqrt{32}$  

Simplify the surd.

•  $2\sqrt{4}$  

•  $4\sqrt{2}$  

•  $4\sqrt{4}$  

•  $2\sqrt{2}$  

 $\frac{5}{\sqrt{2}}$  

Rationalise the denominator

•  $\frac{5}{2}$  

•  $5\sqrt{2}$  

•  $\frac{\sqrt{2}}{4}$  

•  $\frac{5\sqrt{2}}{2}$  

 $\frac{8}{3\sqrt{2}}$  

Rationalise the denominator.

•  $4\sqrt{\frac{2}{3}}$  

•  $\frac{4\sqrt{2}}{3}$  

•  $4\sqrt{2}$  

•  $\frac{4\sqrt{2}}{\sqrt{3}}$  

 $\frac{1}{2+\sqrt{2}}$  

How do you rationalise the denominator?

•  $\times\sqrt{2}$  to numerator and denominator

•  $\times\left(2-\sqrt{2}\right)\$  to denominator

•  $\times\left(2-\sqrt{2}\right)\$  to numerator

•  $\times\left(2-\sqrt{2}\right)\$  to both numerator and denominator