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

Explanation:

Rational number

`1) (4)/(5)+(3)/(8)\\\\(4)/(5) \ \text{is a rational number} \ and \ (3)/(8) \ \text{is a rational number}\\\\(4)/(5)+(3)/(8) \ \text{is also a rational number}`

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

c)

`7√(5)-√(245)=7√(5)-√(7*7*5)`

`= 7√(5)-7√(5)\\\\=0\\\\\text{\bf $ 7√(5)-√(245)$ ia a rational number}`

d)

`(4√(7))*(2√(7))=4*2*√(7*7)\\`

= 4*2*7

= 56

`4√(7)*2√(7) \ \text{\bf is a rational number}`