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

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GreenlightTestPrep
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If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   11 Aug 2019, 10:18
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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) \(1\)

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

e) \(2\)
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   11 Aug 2019, 10:21
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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: \(x = \frac{4}{8} = \frac{1}{2}\)

Answer: B

Cheers,
Brent
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   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: \(x = \frac{4}{8} = \frac{1}{2}\)

Answer: B

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: \((\sqrt[3]{\frac{4}{x}})^3=2^3\)
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   12 Aug 2019, 07:12
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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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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   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.
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   12 Aug 2019, 08:20
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
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   12 Aug 2019, 08:24
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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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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink] New post   16 Feb 2023, 01:49
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Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]
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