ANSWER
The rational numbers are;
B.
[tex]7 \sqrt{5} - \sqrt{245} [/tex]
C.
[tex] \frac{4}{5} + \frac{3}{8} [/tex]
D.
[tex](4 \sqrt{7} )(2 \sqrt{7} )[/tex]
EXPLANATION
The first expression is
[tex]\pi \times \sqrt{36} [/tex]
When we simplify this obtain,
[tex] = \pi \times 6 = 6\pi[/tex]
Since π is an irrational number, all its multiples are also irrational.
The second expression is
[tex]7 \sqrt{5} - \sqrt{245} [/tex]
[tex]7 \sqrt{5} - \sqrt{49 \times 5} [/tex]
We simplify to obtain,
[tex]7 \sqrt{5} - \sqrt{49} \times \sqrt{5} [/tex]
[tex] = 7 \sqrt{5} - 7\sqrt{5} = 0[/tex]
This is a rational number, because
[tex]0 = \frac{0}{1} [/tex]
The third expression is
[tex] \frac{4}{5} + \frac{3}{8} [/tex]
[tex] = \frac{8 \times 4 + 3 \times 5}{40} [/tex]
[tex] = \frac{32 + 15}{40} [/tex]
[tex] = \frac{47}{40} [/tex]
This is also a rational number.
The fourth expression is
[tex](4 \sqrt{7} ) \times (2 \sqrt{7} ) = 4 \times 2 \times \sqrt{7} \times \sqrt{7} [/tex]
[tex] = 8 \times ({ \sqrt{7} })^{2} [/tex]
[tex] = 8 \times 7 = 56[/tex]
This is also a rational number.
The last option is
[tex] \sqrt{100} + \sqrt{5} = 10 + \sqrt{5} [/tex]
The sum of a rational number 10 and an irrational number √5 is an irrational number.
