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If y > 0,which of the following is equal to (48y^3)^(1/2) ?

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If y > 0,which of the following is equal to (48y^3)^(1/2) ? [#permalink] New post   Updated on: 23 Dec 2018, 03:19
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If y > 0 , which of the following is equal to \(\sqrt{48y^3}\)?


(A) \(4y\sqrt{3y}\)

(B) \(3y \sqrt{4y}\)

(C) \(2 \sqrt{12y}\)

(D) \(3 \sqrt{8y}\)

(E) \(16y\sqrt{3y}\)
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A

Originally posted by KSBGC on 05 Aug 2018, 05:12.
Last edited by Bunuel on 23 Dec 2018, 03:19, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If y > 0,which of the following is equal to (48y^3)^(1/2) ? [#permalink] New post   05 Aug 2018, 06:15
selim wrote:
If y>0 , which of the following is equal to \(\sqrt{48y^3}\)?

A) 4y\(\sqrt{3y}\)

B) 3y\(\sqrt{4y}\)

C) 2\(\sqrt{12y}\)

D) 3\(\sqrt{8y}\)

E) 16y\(\sqrt{3y}\)


\(\sqrt{48y^3}\)
=\(\sqrt{48}*\sqrt{y^3}\)
=\(\sqrt{48}*(y^3)^{\frac{1}{2}}\)
=\(\sqrt{48}*y^{\frac{3}{2}}\)
=\(4\sqrt{3}*y^{(1+\frac{1}{2})}\)
=\(4\sqrt{3}*y*y^{\frac{1}{2}}\)
=\(4\sqrt{3}*y*\sqrt{y}\)
=\(4y*\sqrt{3}*\sqrt{y}\)
=\(4y\sqrt{3y}\)

Ans. (A)
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Re: If y > 0,which of the following is equal to (48y^3)^(1/2) ? [#permalink] New post   05 Aug 2018, 07:29
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selim wrote:
If y>0 , which of the following is equal to \(\sqrt{48y^3}\)?

A) 4y\(\sqrt{3y}\)

B) 3y\(\sqrt{4y}\)

C) 2\(\sqrt{12y}\)

D) 3\(\sqrt{8y}\)

E) 16y\(\sqrt{3y}\)

\(\sqrt{48y^3}=\sqrt{(4*4)*3*(y*y)*y}\)
-- \(\sqrt{4*4}=4\)
-- \(\sqrt{y*y}=y\)
-- \(\sqrt{3*y}\) cannot be simplified. Those two terms remain underneath the radical.

\(\sqrt{48y^3}=4*y*\sqrt{3*y}=4y\sqrt{3y}\)

Answer A
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Re: If y > 0, which of the following is equal to (48y^3)^1/2? [#permalink] New post   22 Dec 2018, 08:58
OA -A
on splitting the number inside the square into perfect square we get 4y out of square and 3y inside the root

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If y > 0, which of the following is equal to (48y^3)^1/2? [#permalink] New post   22 Dec 2018, 14:58
HKD1710 wrote:
If \(y > 0\), which of the following is equal to \(\sqrt{48y^3}\)?

(A) \(4y\sqrt{3y}\)
(B) \(3y\sqrt{4y}\)
(e) \(2\sqrt{12y}\)
(D) \(3\sqrt{8y}\)
(E) \(16y\sqrt{3y}\)

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\(\sqrt{48y^3}\)

=\(\sqrt{16*3*y^2*y}\)

=4y \(\sqrt{3y}\)

A is the correct answer.
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Re: If y > 0,which of the following is equal to (48y^3)^(1/2) ? [#permalink] New post   12 Jun 2021, 10:10
Instead of solving this equation a quick look at the answer choices will give you the answer.

The first choice \(4y\sqrt{3y}\)
\(4y\) when squared will give \(16y^2\) and multiply that with \(3y\) and you will get \(48y^3\)

Hence answer is A.
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Re: If y > 0,which of the following is equal to (48y^3)^(1/2) ? [#permalink] New post   29 Jan 2024, 08:20
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Re: If y > 0,which of the following is equal to (48y^3)^(1/2) ? [#permalink]
29 Jan 2024, 08:20
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