List of practice Questions

Classify the following numbers as rational or irrational:

(i) \(2 - \sqrt5\)  

(ii) \((3 + \sqrt23) - \sqrt23\) 

(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)

(iv) \(\frac{1}{\sqrt{2}}\)

(v) 2π 

Simplify each of the following expressions: 

(i) (3 + √3)(2 + √2) 

(ii) (3 + √3)(3 - √3) 

(iii) (√5 + √2 )2 

(iv) (√5 - √2)(√5 + √2)

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π =\(\frac{ c}{d}\). This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Represent √9.3 on the number line

Rationalise the denominators of the following: 

(i) \(\frac{1 }{ \sqrt{7 }}\)

(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)

(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)

(iv) \(\frac{1 }{ \sqrt{7}-2}\)