The number (2 – √3)2 is:

The number (2 – √3)² is

(a) A natural number

(b) An integer

(c) A rational number

(d) An irrational number

Solution:

(d) An irrational number is correct

Hint : (2 – √3)² = 2² – 2 × 2 ×√3 + (√3)²

= 4 – 4√3 + 3

= 7 – 4√3 is an irrational number

If x a positive rational number which is not a perfect square, then -5√x is

(a) A negative integer

(b) An integer

(c) A rational number

(d) An irrational number

Solution:

(d) Irrational number

More Solutions:

• Express the following numbers in the form p/q.
• Classify the following numbers as rational or irrational:
• what can you say about the prime factors of q?
• Insert an irrational number between the following.
• Insert two irrational numbers between 2 and 3.
• Find one rational number between √2 and √3.
• Insert irrational numbers between √5 and √7.
• Simplify the following: (i) √45 – 3√20 + 4√5
• Simplify the following: (i) (5 + √7) (2 + √5).