Radicals & rational expressions, worked out

The Root Cellar

Dig the perfect squares out from under the root. Simplify square roots and cube roots, add and multiply radicals, rationalize denominators, trade roots for fractional exponents, solve radical equations, and simplify, multiply, add and solve rational expressions — checking every answer for the ones that don’t really work, with the reason for every step.

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The work

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    Every number is kept exact (whole numbers, fractions and roots), with decimals alongside.