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

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

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New post 05 Aug 2018, 04:12
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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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If y>0,which of the following is equal to [m][square_root]48y^3[/squ  [#permalink]

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

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New post 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.

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

Answer A
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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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