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# If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square_root]22[/

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11 Aug 2019, 11:15
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Difficulty:

55% (hard)

Question Stats:

59% (01:46) correct 41% (01:45) wrong based on 32 sessions

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If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$\sqrt[3]{\frac{1}{2}}$$

D) $$\sqrt[3]{2}$$

e) $$2$$

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11 Aug 2019, 12:05
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X^1/3= (4^1/3 * 5.5^1/2)/22^1/2
X^1/3=4^-1/6
(X^1/3)^3=(4^-1/6)^3
X=4^-1/2
X=√1/4=1/2
Option B

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12 Aug 2019, 09:29
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GMATPrepNow wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$\sqrt[3]{\frac{1}{2}}$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Useful root property: $$\frac{\sqrt[n]{x}}{\sqrt[n]{y}}=\sqrt[n]{\frac{x}{y}}$$

Given: $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

Divide both sides by $$\sqrt{5.5}$$ to get: $$\sqrt[3]{4}=\frac{(\sqrt{22})(\sqrt[3]{x})}{\sqrt{5.5}}$$

Divide both sides by $$\sqrt[3]{x}$$ to get: $$\frac{\sqrt[3]{4}}{\sqrt[3]{x}}=\frac{\sqrt{22}}{\sqrt{5.5}}$$

Apply above property to both sides to get: $$\sqrt[3]{\frac{4}{x}}=\sqrt{\frac{22}{5.5}}$$

Simplify right side: $$\sqrt[3]{\frac{4}{x}}=\sqrt{4}$$

Simplify right side: $$\sqrt[3]{\frac{4}{x}}=2$$

Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^3$$

Simplify: $$\frac{4}{x} = 8$$

Solve: $$x = \frac{4}{8} = \frac{1}{2}$$

Cheers,
Brent
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12 Aug 2019, 10:18
GMATPrepNow wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$\sqrt[3]{\frac{1}{2}}$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Given: $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

$$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$
$$(\sqrt[3]{4})=2(\sqrt[3]{x})$$ since 22=5.5*4 => $$\sqrt{22} = 2\sqrt{5.5}$$
4 = 8 x
$$x= \frac{4}{8} = \frac{1}{2}$$

IMO B
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square_root]22[/   [#permalink] 12 Aug 2019, 10:18
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