Question

is the following number rational or irrational?\\(\sqrt{200}\\)\
choose 1 answer:\
a rational\
b irrational

Explanation:

Step1: Simplify the square root

$\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}$

Step2: Identify nature of $\sqrt{2}$

$\sqrt{2}$ is an irrational number (cannot be written as a fraction of two integers). Multiplying a non-zero rational number ($10$) by an irrational number results in an irrational number.

Answer:

B. Irrational