Question

Prove that √(3*5^-3) ÷ 3√(3^-1*5) * 6√(3*5^5) = 3÷5

Answer 1

Given: { √(3*5^-3) ÷ (∛3^-1 x √5) } * 6th root of ( 3 x 5^6 )  =  3÷5

To find: Prove that LHS = RHS in above problem.

Solution:

• Now, first lets start solving from LHS side, we get :

• LHS :   { √(3*5^-3) ÷ (∛3^-1 x √5) } * 6th root of ( 3 x 5^6 )

• Simplify all the powers, we get:

                 { (3 x 5^-3) ^1/2  ÷  (3^-1) ^1/3 (5)^1/2 } x  (3 x 5^6)^1/6

                 { (3)^1/2 x (5^-3) ^1/2  ÷  (3^-1) ^1/3 (5)^1/2 } x  (3 x 5^6)^1/6

• Simplifying both the two brackets simultaneously now, we get:

                 { (3)^1/2 x (5)^-3/2  ÷  (3) ^-1/3 (5)^1/2 } x  ((3)^1/6 x (5)^6/6)

                 { (3)^1/2 - (-1/3) x (5)^(-3/2-1/2) } x  ((3)^1/6 x (5))

                 { (3)^(3+2/6) x (5)^(-4/2) } x  ((3)^1/6 x (5))

                 { (3)^(5/6) x (5)^(-2) } x  ((3)^1/6 x (5))

• Now, combining both the brackets together we get:

                 { (3)^(5/6 + 1/6) x (5)^(-2 + 1)  }

                 { (3)^(6/6) x (5)^(-1)  }

                 { (3)x (5)^(-1)  }

                 { (3)x (1/5)  }

                 { 3/5 }       ................... RHS

Answer:

                So from the above terms we have proved that LHS = RHS

                { √(3*5^-3) ÷ (∛3^-1 x √5) } * 6th root of ( 3 x 5^6 )  =  3÷5

                Hence proved.

Answer 2

Answer:

3/5 is the answer ok ok ol