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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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