Problem

Subtract. Simplify by collecting like radical terms if possible.
\[
2 \sqrt{32}-5 \sqrt{2}
\]
\[
2 \sqrt{32}-5 \sqrt{2}=\square
\]
(Simplify your answer. Type an exact answer, using radicals as needed.)

Answer

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Answer

Final Answer: \( \boxed{4 \sqrt{2}} \)

Steps

Step 1 :First, we simplify the square root of 32. We can do this by finding the prime factorization of 32 and then simplifying the square root.

Step 2 :Next, we subtract 5 times the square root of 2 from the simplified square root of 32.

Step 3 :The result of the calculation is approximately 4.24. However, the question asks for an exact answer using radicals as needed. Therefore, we need to simplify the square root of 32 in terms of square roots of prime numbers.

Step 4 :The result of the calculation is approximately 4.24, which is the same as the previous calculation. However, this result is in terms of square roots of prime numbers, which is what the question asks for.

Step 5 :Therefore, the exact answer to the question is 4 times the square root of 2.

Step 6 :Final Answer: \( \boxed{4 \sqrt{2}} \)

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