Complete the following exercise:
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Complete the following exercise:
To solve the problem , we will work through it step by step:
Step 1: Simplify the inner square roots.
Step 2: Evaluate the cube roots.
Step 3: Multiply the results of the cube roots.
Thus, the simplified expression is .
Therefore, the solution to the problem is .
Choose the largest value
Because the radicals are nested! You have square roots inside cube roots, so you must follow the order of operations and simplify from the inside out. Multiplying 25 × 64 = 1600 first would give you a completely different problem.
Look for perfect cubes! Numbers like 1, 8, 27, 64, 125 have cube roots that are whole numbers. Since , we know .
If you get something like , partially simplify it to first, then take the cube root. The process is the same - always simplify inner radicals before outer ones!
While calculators help check your work, practice doing these by hand first! Recognizing perfect squares (25 = 5²) and perfect cubes (8 = 2³) builds your number sense and makes you faster at mental math.
Because is an irrational number that doesn't have a nice decimal form. Leaving it in radical form gives the exact answer, which is more precise than a rounded decimal approximation.
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