Question

How to calculate `6(sqrt5)^5 (2) =300(sqrt 5)?`

Answer 1

See the answer and proofing in the explanation below:

`(5^(5/2))/5^(1/2) = 25`
`5^(4/2)=25`
`5^2=25`
`25=25`

Explanation:

We can use exponential law to simplify this equation.

`sqrt(a) = a^(1/2)`
`(sqrt(a))^2 = a^(1/2xx2)` = `a^1 = a`

`6(sqrt(5))^2(2) = 300(sqrt(5))`

`6xx2xxsqrt(5)^5 = 300sqrt(5)`

`12xxsqrt(5)^5 = 300sqrt(5)`

`(sqrt(5)^5)/sqrt(5) = 300/12`

`(sqrt(5)xxsqrt(5)xxsqrt(5)xxsqrt(5)xxsqrt(5))/sqrt(5) = 25`

`(sqrt(5)xxsqrt(5)xxsqrt(5)xxsqrt(5)xxcancelsqrt(5))/cancelsqrt(5) = 25`

We know that `sqrt(a) xx sqrt(a) = a`

`(sqrt(5)xxsqrt(5)xxsqrt(5)xxsqrt(5))= 25`

`5xx5=25`
`25=25`