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 .
Solve the following exercise:
\( \sqrt{\frac{2}{4}}= \)
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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