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# If y>0,which of the following is equal to [m][square_root]48y^3[/squ

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Director
Joined: 31 Oct 2013
Posts: 897
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If y>0,which of the following is equal to [m][square_root]48y^3[/squ  [#permalink]

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05 Aug 2018, 04:12
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Question Stats:

86% (00:53) correct 14% (01:25) wrong based on 28 sessions

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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$$\sqrt{3y}$$
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
If y>0,which of the following is equal to [m][square_root]48y^3[/squ  [#permalink]

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05 Aug 2018, 05:15
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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PKN

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Joined: 22 May 2016
Posts: 2222
If y>0,which of the following is equal to [m][square_root]48y^3[/squ  [#permalink]

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05 Aug 2018, 06:29
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.

$$\sqrt{48y^3}=4*y*\sqrt{3*y}=4y\sqrt{3y}$$

If y>0,which of the following is equal to [m][square_root]48y^3[/squ &nbs [#permalink] 05 Aug 2018, 06:29
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