Question
Is \( \sqrt{32} \) an irrational number? yes no
Ask by Gross Macdonald. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
√32 is an irrational number.
Solution
First, note that √32 can be simplified:
√32 = √(16×2) = √16 × √2 = 4√2
Since √2 is known to be an irrational number, multiplying it by 4 (a rational number) still results in an irrational number. Thus, 4√2 is irrational.
The answer is: yes, √32 is an irrational number.
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Simplify this solution The Deep Dive
Yes, \( \sqrt{32} \) is not an irrational number. In fact, \( \sqrt{32} \) simplifies to \( 4\sqrt{2} \) because \( 32 = 16 \times 2 \). Since \( \sqrt{2} \) is known to be an irrational number, multiplying it by the rational number 4 still leaves us with an irrational result. When we break it down further, you can see that \( 4\sqrt{2} \approx 4 \times 1.414 \), which is about 5.656. So whenever you encounter the square root of a non-perfect square and it doesn’t reduce to an integer, you’re likely dealing with an irrational number.
