simplify the equation

Question

simplify 5√(50)/3+√(2) - 3√(18)

Answer 1

(5√50)/3 = 5√(5²)(2)/3 = (25√2)/3

3√18 = 3√(3²)(2) = 9√2 

 

So we combine like terms, noting that 9√2 = (27√2)/3 and √2 = (3√2)/3:

 

(25√2)/3 + (3√2)/3 - (27√2)/3 = (√2)/3

 

 

 

Answer 2

Factor each of the numbers inside the radical signs to s see what happens:

 

5√(50)/3+√(2) - 3√(18)

 

5√(50)/3 = 5√(25* 2) / 3 = 5√(25) * √(2) / 3 = 5 * 5 * √2 / 3 = (25/3) √2

 

3√(18) = 3√(9 * 2) - 3 √(9) * √(2)= 3 * 3 * √2 = 9 √2

 

So now we have:

 

5√(50)/3+√(2) - 3√(18) =

(25/3) √2 + √2 - 9 √2 =

(25/3 + 1 - 9)√2 =

(25/3 + 3/3 - 27/3)√2 =

(1/3)√2 = 

√2/3