Decreasing the Nesting Depth of Expressions Involving Square Roots

We develop the theory for decreasing the depth of nesting in expressions that contain square roots We show exactly when fourth roots enable denesting of expresstons not denestable with square roots only When we restrict our attention to denesting over the real numbers, we show in fact that no roots other than square roots or fourth roots are ever useful for denesting expressions containing square roots only, thus characterising the denestable expressions in thls case We then proceed to describe new algorithms that accomplish such denesting