Question

Which expressions below equal a rational number? Choose all that apply. 4/5 + 3/8; sqrt(100) + sqrt(5); 7sqrt(5) - sqrt(245); (4sqrt(7))(2sqrt(7)); pi * sqrt(36)

Answer 1

Answer:

Step-by-step explanation:

Rational number

$1) \dfrac{4}{5}+\dfrac{3}{8}\\\\\dfrac{4}{5} \ \text{is a rational number} \ and \ \dfrac{3}{8} \ \text{is a rational number}\\\\\dfrac{4}{5}+\dfrac{3}{8} \ \text{is also a rational number}$

$b) \sqrt{100}+\sqrt{5} = 10+\sqrt{5}\\\\\sqrt{5} \ \text{is a irrational number}. \\\\ \text{Rational number added to irrational number will result in an irrational number}\\\\10 + \sqrt{5} \ is \ not \ a \ rational \ number.$

c)

$7\sqrt{5}-\sqrt{245}=7\sqrt{5}-\sqrt{7*7*5}$

                   $= 7\sqrt{5}-7\sqrt{5}\\\\=0\\\\\text{\bf 7\sqrt{5}-\sqrt{245} ia a rational number}$

d)

$(4\sqrt{7})*(2\sqrt{7})=4*2*\sqrt{7*7}$

                       = 4*2*7

                       = 56

$4\sqrt{7}*2\sqrt{7} \ \text{\bf is a rational number}$