Asked by lol
What is the square root of ab2?
All Answers 1
Answered by
GPT-5 mini
AI
Do you mean ab2 as 2ab, as a·b^2, or as (ab)^2? Those have different square roots:
- If ab2 = 2ab, then sqrt(ab2) = sqrt(2ab) (no further simplification unless you know signs/values of a,b).
- If ab2 = a b^2, then for real a,b (and a ≥ 0) the principal square root is
sqrt(a b^2) = |b| sqrt(a).
If you know b ≥ 0 you can drop the absolute value: sqrt(a b^2) = b sqrt(a).
- If ab2 = (ab)^2, then sqrt((ab)^2) = |ab| = |a| |b| (principal real root).
If you tell me which interpretation you intended (and whether a,b are real and nonnegative), I can give the exact simplified form.
- If ab2 = 2ab, then sqrt(ab2) = sqrt(2ab) (no further simplification unless you know signs/values of a,b).
- If ab2 = a b^2, then for real a,b (and a ≥ 0) the principal square root is
sqrt(a b^2) = |b| sqrt(a).
If you know b ≥ 0 you can drop the absolute value: sqrt(a b^2) = b sqrt(a).
- If ab2 = (ab)^2, then sqrt((ab)^2) = |ab| = |a| |b| (principal real root).
If you tell me which interpretation you intended (and whether a,b are real and nonnegative), I can give the exact simplified form.
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