# Which expressions below equal a rational number? (a) 2√2 - √8 (b) 5√3 × 2√3 (c) 2√2 ÷ 2

**Solution:**

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0.

(a) 2**√**2 - **√**8

⇒ 2**√**2 - 2**√**2 = 0 (Since, **√**8 = 2**√**2 )

0 is a rational number because it can be written as 0/1.

(b) 5**√**3 × 2**√**3

⇒ 5 × 2 × **√**3 × **√**3

⇒ 5 × 2 × **√**9

⇒ 5 × 2 × 3 = 30

All natural numbers are rational numbers.

So, 30 is a rational number.

(c) 2**√**2 ÷ 2 = **√**2

**√**2 is an irrational number as its decimal expansion is non terminating non-repeating.

Thus, the rational numbers are (a) 2**√**2 - **√**8, and (b) 5**√**3 × 2**√**3.

## Which expressions below equal a rational number? (a) 2√2 - √8 (b) 5√3 × 2√3 (c) 2√2 ÷ 2

**Summary:**

The expressions that are rational numbers are (a) 2**√**2 - **√**8, and (b) 5**√**3 × 2**√**3.

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