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

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GRE Instructor
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If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  11 Aug 2019, 10:18
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Question Stats:

33% (00:45) correct 66% (00:46) wrong based on 3 sessions
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

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

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

C) $$1$$

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

e) $$2$$
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
Posts: 2290
Followers: 71

Kudos [?]: 2165 [1] , given: 26

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  11 Aug 2019, 10:21
1
KUDOS
Expert's post
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

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

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

C) $$1$$

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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Manager
Joined: 22 Jun 2019
Posts: 106
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Kudos [?]: 12 [0], given: 34

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 01:42
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

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

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

C) $$1$$

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: $$(\sqrt[3]{\frac{4}{x}})^3=2^2$$

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

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

Cheers,
Brent

I think,seems little mistake in the last portion. It will be
Corrected line: Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^3$$
Director
Joined: 20 Apr 2016
Posts: 960
WE: Engineering (Energy and Utilities)
Followers: 13

Kudos [?]: 743 [1] , given: 155

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 07:12
1
KUDOS
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

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

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

C) $$1$$

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

e) $$2$$

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

or $$(\sqrt[3]{4}) * 2.3 = 4.6* (\sqrt[3]{x})$$ { use of calculator to find $$\sqrt{5.5}$$ and $$\sqrt{22}$$ }

or $$(\sqrt[3]{4}) = 2 * (\sqrt[3]{x})$$ (dividing both sides by 2.3)

Cubing both sides
$$4 = 8* x$$

or $$x = \frac{1}{2}$$
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Manager
Joined: 22 Jun 2019
Posts: 106
Followers: 0

Kudos [?]: 12 [0], given: 34

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 07:37
pranab01 wrote:
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

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

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

C) $$1$$

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

e) $$2$$

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

or $$(\sqrt[3]{4}) * 2.3 = 4.6* (\sqrt[3]{x})$$ { use of calculator to find $$\sqrt{5.5}$$ and $$\sqrt{22}$$ }

or $$(\sqrt[3]{4}) = 2 * (\sqrt[3]{x})$$ (dividing both sides by 2.3)

Cubing both sides
$$4 = 8* x$$

or $$x = \frac{1}{2}$$

I THINK GRE CALCULATOR DOES NOT ALLOW TO CALCULATE ROOT EITHER, SO WE NEED TO PASS IT.
GRE Instructor
Joined: 10 Apr 2015
Posts: 2290
Followers: 71

Kudos [?]: 2165 [0], given: 26

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 08:20
Expert's post
huda wrote:
I think,seems little mistake in the last portion. It will be
Corrected line: Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^3$$

Good catch - thanks!
I've changed the exponent.

Kudos for you!!

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for my free GRE Question of the Day emails

GRE Instructor
Joined: 10 Apr 2015
Posts: 2290
Followers: 71

Kudos [?]: 2165 [1] , given: 26

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 08:24
1
KUDOS
Expert's post
huda wrote:
pranab01 wrote:
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

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

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

C) $$1$$

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

e) $$2$$

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

or $$(\sqrt[3]{4}) * 2.3 = 4.6* (\sqrt[3]{x})$$ { use of calculator to find $$\sqrt{5.5}$$ and $$\sqrt{22}$$ }

or $$(\sqrt[3]{4}) = 2 * (\sqrt[3]{x})$$ (dividing both sides by 2.3)

Cubing both sides
$$4 = 8* x$$

or $$x = \frac{1}{2}$$

I THINK GRE CALCULATOR DOES NOT ALLOW TO CALCULATE ROOT EITHER, SO WE NEED TO PASS IT.

pranab01 is estimating those roots.
It's a good strategy.

By the way, the GRE's onscreen calculator does have a square root button.
Here's my video on this
[you-tube]https://youtu.be/qvL9uwnR0v8[/you-tube]

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square   [#permalink] 12 Aug 2019, 08:24
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