Find a+b if: ( √(2) + √(3)) / 3 √(2) = a + b √(6) ​

Question

Find a+b if:


`( √(2) + √(3)) / 3 √(2) = a + b √(6)`
​

Answer 1

• 1/2

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Simplify the left side of the equality:

• 
  `(√(2) +√(3)) /3√(2) =`

• 
  `√(2) /3√(2) +√(3)) /3√(2) =` Distribute

• 
  `1/3+1/√(3*2)=` Simplify

• 
  `1/3+1/√(6)=` Make denominator rational

• 
  `1/3+√(6)/ 6`

Comparing this with the right side, we see that:

• a = 1/3 and b = 1/6

Find the sum:

• a + b =
• 1/3 + 1/6 =
• 2/6 + 1/6 =
• 3/6 =
• 1/2