Question

√(3×5^(−3)÷3×√(3^(−1)×√(5)×6×√(3×5^(6) = 3/5. prove tha​

Answer 1

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.

Step-by-step explanation:

olution:

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

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