Surds Worksheet

Simplify the following surd...

• 3√2

• 2√3

• 9√2

• 3√6

Simplify the following surd...

• 7√2

• 3√5

• 9√3

• 3√3

Simplify fully: 
√32 + 5√32

• 6√32
• 24√8
• 24√2
• 6√8

Tags

CCSS.HSN.RN.A.2

Rationalise the Denominator:
^{(3 + √4)} /_√2

• ^5√2/₂
• ^{(3√2 +√8)} /₂
• ^{(3√2 +√8)} /4 
• ^{(3√2 + √3 )} /₂

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Fully simplify....

• 
• 
• 
• 

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

What should you multiply $\frac{6}{1-\sqrt{5}}$  by to rationalize the denominator?

• -4

•  $1-\sqrt{5}$  

•  $1+\sqrt{5}$  

•  $-\frac{\left(3-3\sqrt{5}\right)}{2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Rationalize the following: $\frac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}$  

•  $\frac{\sqrt{6}-\sqrt{10}}{8}$  

•  $\frac{\sqrt{6}-\sqrt{10}}{-2}$  

•  $\frac{\sqrt{6}+\sqrt{10}}{8}$  

•  $\frac{2\sqrt{3}+2\sqrt{5}}{-2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSN.RN.A.2

 $\frac{3+5\sqrt{3}}{4-2\sqrt{3}}$  Rationalize:

•  $\frac{-9+7\sqrt{3}}{2}$  

•  $\frac{-18+14\sqrt{3}}{4}$  

•  $\frac{21+13\sqrt{3}}{2}$  

•  $\frac{24-26\sqrt{3}}{4}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

 $\frac{\sqrt{3}-\sqrt{7}}{\sqrt{3}+\sqrt{7}}$  

•  $\frac{5-\sqrt{21}}{-2}$  

•  $\frac{10-\sqrt{21}}{-2}$  

•  $\frac{5-2\sqrt{21}}{-2}$  

•  $-\frac{4}{10}=-\frac{2}{5}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

1.       If a and b are positive integers, which of the following is/are correct?


 $I.\sqrt{a^2+b^2}=a+b$  

 $II.\sqrt{a^2b^2}=ab$  
 $III.\sqrt{2a^2b}\times\sqrt{6a^3b}=2a^2b\sqrt{3a}$  

• II only

• III only
  

• II and III only
  

• I, II and III