Answer: The answer is: " 4√2 " .
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Explanation:
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" √32 " can be factored into:
"√16 * √2 " ;
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√16 = 4 ;
→ Rewrite as "4√2 " .
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Note: Given: "Find: √32 " ;
We shall assume "positive factors" ;
Factors of 32 include:
32: 1, 32, 2, 16, 4, 8 .
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√32 = √1 * √32 ; = √32 ? No; that just leads to where we already are.
√32 = √2 * √16 ? ; Yes; since √16 = 4 (perfect square);
→ so: 4*√2; or " 4√2 " .
This is the easiest way.
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What about:
√32 = √8 * √4 ? Yes; we can also use this method:
→ √32 = √8 * √4 = √8 *2 ; {since √4 = 2 (perfect square);
↔ 2√8 ;
Note: √8 = √4 *√2 = 2√2 ; {since √4 = 2 (perfect square);
→ √8 = 2√2 ;
→ 2√8 = 2 * 2√2 ;
= 4√2 ; which is our answer.
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