simplify expression and solve equation

Question

 

Woud you please help simplify and solve:

 

√x (√9 - 4/3) = √25

Answer 1

As written:

√x (√9 - 4/3) = √25     First solve the two known radicals (this leaves us with multiple possibilities)

√x (±3 - 4/3) = ±5       Next simplify the parentheses

√x (5/3) = ±5   and   √x (-13/3) = ±5      Now multiply both sides by 3

√x (5) = ±15   and   √x (-13) = ±15          Then divide by 5 and -13 respectively

√x = ±3   and   √x = ±15/13                      Finally, square both side of the equation

 

x = 9   and   x ≈ 1.33       Now it's good to check your answer

 

If you plug x ≈ 1.33 into the original equation, it doesn't work so in this case there is only one answer.

 

x = 9

 

-Mike-

Answer 2

√x (√(9) - 4/3) = √(25)

 

√x (3 - 4/3) = 5

 

Multiply both sides by 3:

 

√x (9 - 4) = 15

 

5√x = 15

 

Divide both sides by 5:

 

√x = 3

 

Square both sides:

 

x = 9

Answer 3

√[x ( √9 - 4/3 ) ]  = √25

 

X ( 9 - 4/3 ) = 25

 

X ( 23/3 ) = 25

 

  X = 25 * 3/23 = 75/23

 

      Or:

 

 ^{√X . ( √9 - 4/3) = √25}

 

   X [( 3 - 4/3 ) ^2] = 25

   

     X =        25         =

            ( 3 - 4/3)^2

 

                     25       =

                (5/3) ^2

 

                    9(25)         =  9

                      25