Question

Which number is a rational number

Answer 1

square root of 49 i think

Answer 2

`\sqrt{ (36)/(16) }`

Explanation:

A rational number is one that can be expressed as a fraction.

• 
  `\sqrt{ (36)/(6) } = √(6)`
• sqrt(6) is irrational.

Therefore, top left and right and irrational.

Bottom left:

• 
  `\sqrt{ (36)/(16) } = ( √(36) )/( √(16) ) = (6)/(4) = (3)/(2)`
• Very obviously already in a fractional form making it rational.

Bottom right:

• 
  `\sqrt{ (16)/(6) } = ( √(16) )/( √(6)) = (4)/( √(6) ) = (4 √(6) )/(6) = (2 √(6) )/(3)`
• We already established that the sqrt(6) is not rational, so this expression is also irrational.