Brackets make this clearer

λ = h/[m*√(2E/m)]

Using m = √(m^2)

λ = h/[√[(2E/m) *(m^2)]

λ = h/√(2mE)

Needs parentheses! Do you mean

λ = h/(m·√(2E/m)) ?

https://www.flickr.com/photos/dwread/32367508600/

I assume you mean:

λ = h / [m √(2E/m)] ----> λ = h / √(2Em)

That's because m / √m = m^1 / m^(1/2) = m^(1−1/2) = m^(1/2) = √m

Therefore, m √(2E/m) = √(2Em)