Which statement is always true ?
Every whole number is rational
Every whole number (0, 1, 2, 3, ...) can be written as a fraction with denominator 1, for example \(5 = \frac{5}{1}\), so it satisfies the definition of a rational number.
Natural numbers are a subset of rational numbers, not irrational, so the second statement is false.
Rational numbers include negative and fractional values (like -3 or 1/2), which are neither natural nor whole numbers, so the third and fourth statements are false.
Every whole number is rational is always true.
Important Questions from Rational or Irrational Numbers
If \(\sqrt{1+\frac{\sqrt{3}}{2}}- \sqrt{1-\frac{\sqrt{3}}{2}}= c\) , then the value of c is:
If \(\frac{\sqrt{38-5\sqrt{3} } }{\sqrt{26+7\sqrt{3} } }= \frac{a+b\sqrt{3} }{23} \) , b > 0, then the value of (b – a) is:
If \( \frac{5}{4{\sqrt 2 }} + \frac{{3 + 2\sqrt 2 }}{{3 - 2\sqrt 2 }} - \frac{{3 - 2\sqrt 2 }}{{3 + 2\sqrt 2 }} = a + b\sqrt 2 \) , then what is the value of (3a + 4b)?
If \(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5} = a\sqrt 3 - b,\) then the value of a + b is equal to:
If \(\frac{\sqrt{26-7\sqrt{3} } }{\sqrt{14+5\sqrt{3} } } = \frac{b+a\sqrt{3} }{11}\) , b > 0, then what is the value of \(\sqrt{(b-a)} \) ?
