#### 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} = 2^{2} – 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).