diff --git a/src/optimise/optimisers.jl b/src/optimise/optimisers.jl
index 2accc4bc..d750a848 100644
--- a/src/optimise/optimisers.jl
+++ b/src/optimise/optimisers.jl
@@ -149,7 +149,7 @@ function update!(o::ADAGrad, x, Δ)
   η = o.eta
   acc = get!(o.acc, x, fill(ϵ, size(x)))::typeof(x)
   @. acc += Δ^2
-  @. Δ *= η / √(acc + ϵ)
+  @. Δ *= η / (√acc + ϵ)
 end
 
 """
@@ -169,7 +169,7 @@ function update!(o::ADADelta, x, Δ)
   ρ = o.rho
   acc, Δacc = get!(o.state, x, (zero(x), zero(x)))
   @. acc = ρ * acc + (1 - ρ) * Δ^2
-  @. Δ *= √(Δacc + ϵ) / √(acc + ϵ)
+  @. Δ *= √Δacc/ (√acc + ϵ)
   @. Δacc = ρ * Δacc + (1 - ρ) * Δ^2
   return Δ
 end
@@ -194,7 +194,7 @@ function update!(o::AMSGrad, x, Δ)
   @. mt = β[1] * mt + (1 - β[1]) * Δ
   @. vt = β[2] * vt + (1 - β[2]) * Δ ^ 2
   @. v̂t = max.(v̂t, vt)
-  @. Δ = η * mt / √v̂t
+  @. Δ = η * mt / (√v̂t + ϵ)
 end
 
 """
@@ -217,7 +217,7 @@ function update!(o::NADAM, x, Δ)
   mt, vt = get!(o.state, x, (zero(x), zero(x)))
   @. mt = β[1] * mt + (1 - β[1]) * Δ
   @. vt = β[2] * vt + (1 - β[2]) * Δ^2
-  @. Δ = (β[1] * mt / (1 - β[1] * β1p) + (1 - β[1]) * Δ / (1 - β1p)) / √(vt * β[2] / (1 - β2p) + ϵ) * η
+  @. Δ = (β[1] * mt / (1 - β[1] * β1p) + (1 - β[1]) * Δ / (1 - β1p)) / (√(vt * β[2] / (1 - β2p)) + ϵ) * η
   o.state[x] = (mt, vt, (β1p * β[1], β2p * β[2]))
   return Δ
 end