alleryWhich of the following is an irrational number?
A$0.\overline{27}$
B$\sqrt{2} + \sqrt{3}$
C$\dfrac{22}{7}$
D$\sqrt{16}$
Answer & Solution
Correct answer: B. $\sqrt{2} + \sqrt{3}$
$\sqrt{16}=4$ (rational), $0.\overline{27}$ is repeating (rational), $22/7$ is a fraction (rational).
$\sqrt2+\sqrt3$ is irrational — if it equalled a rational $r$, squaring gives $5 + 2\sqrt6 = r^2$, forcing $\sqrt6$ rational, a contradiction.
Keep practising Unit 1B2: Algebraic Limits and Continuity
Browse all Unit 1B2: Algebraic Limits and Continuity questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
The decimal expansion of $\dfrac{257}{2^3 \cdot 5^4}$ terminates after how many decimal plThe product of the HCF and LCM of 6 and 20 is:The remainder when $2^{100}$ is divided by 7 isHow many positive integers less than 1000 are divisible by neither 2 nor 5?The HCF of two consecutive positive integers isIf $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(The smallest positive integer that is divisible by every integer from 1 to 10 isThe largest number that divides 245 and 1029, leaving remainders 5 and 5 respectively, is