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Sub 505 (Easy)|   Algebra|   Roots|      
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Bunuel
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For the equation shown above, what is the value of x ? 14 Oct 2020, 00:15
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C
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89% (01:21) correct 11% (02:19) wrong based on 199 sessions

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\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)

For the equation shown above, what could be the value of x ?

A. 6

B. 7

C. 8

D. 12

E. 14


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C
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rajatchopra1994
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For the equation shown above, what is the value of x ? 14 Oct 2020, 02:55
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Explanation:

\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)
\((4 +\sqrt[3]{x})^2 = 6^2\)
Square root both side:
\((\sqrt[3]{x}) =6-4\)
\((\sqrt[3]{x}) =2\)
Cube both side.
x=2^3
x=8

IMO-C
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For the equation shown above, what is the value of x ? 14 Oct 2020, 04:19
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Quote:
\((\sqrt[3]{64} +\sqrt[3]x)^2\)=36
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Step 1: Understanding the question
\(\sqrt[3]{64}\) = 4

\((4 + \sqrt[3]x)^2\) = 36

4 + \(\sqrt[3]x\) = ±6
As sum of 4 and \(\sqrt[3]x\) is an integer, \(\sqrt[3]x\) is integer

As per options only when x = 8, \(\sqrt[3]x\) = \(\sqrt[3]8\) = 2

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For the equation shown above, what is the value of x ? 14 Oct 2020, 04:23
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4 + cube root (x) = +- 6;
If +
4 + cube root (x) = 6
=>cube root (x) = 2
=> x = 8
If -
4 + cube root (x) = -6
cube root (x) = -10
x = (-10)^3
or x = -1000

As per options , C.
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For the equation shown above, what is the value of x ? 15 Oct 2020, 02:29
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\((\sqrt[3]{64} + \sqrt[3]{x})^2 = 36\)

=> \((\sqrt[3]{64} + \sqrt[3]{x})^2 = 6^2\)

=> \((\sqrt[3]{64} + \sqrt[3]{x}) = 6\)

=> \((4 + \sqrt[3]{x})^2 = 6\)

=> (\(\sqrt[3]{x}) = 6 - 4 = 2\)

=> x = \(2^3 = 8\)

Answer C
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For the equation shown above, what is the value of x ? 16 Oct 2020, 05:39
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I have a question. Can the value of RHS be negative i.e -6. Although the expression can give us two possible values, as we have square root on LHS -6 is impossible. So even if the options have the value -1000, the right answer will be 8 right. Please correct me if i am wrong.

Bunuel
\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)

For the equation shown above, what is the value of x ?

A. 6

B. 7

C. 8

D. 12

E. 14


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For the equation shown above, what is the value of x ? 16 Oct 2020, 09:40
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minns
I have a question. Can the value of RHS be negative i.e -6. Although the expression can give us two possible values, as we have square root on LHS -6 is impossible. So even if the options have the value -1000, the right answer will be 8 right. Please correct me if i am wrong.

Bunuel
\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)

For the equation shown above, what is the value of x ?

Show more

I think the wording of this question was fixed -- the equation has two solutions, so it needs to ask "what could be the value of x" if only one of those two solutions will appear among the answer choices. A lot of the posts above I'm guessing quoted the question before it was edited.

If an equation says:

y^2 = 36

then that equation has two solutions; y can be 6 or -6. That's what is happening here:

\(\\
\sqrt[3](64) + \sqrt[3]{x} = 6\\
\)

or

\(\\
\sqrt[3](64) + \sqrt[3]{x} = -6\\
\)

The first equation above has the solution x = 8. The second equation, though, also has a solution, x = -1000. We're taking a cube root in that equation, not a square root, and it's perfectly fine to take a cube root of a negative number.
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For the equation shown above, what is the value of x ? 16 Oct 2020, 10:17
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\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)

Asked: For the equation shown above, what could be the value of x ?

\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)
\((4 + \sqrt[3]x)^2 = 36\)
When x = 8
\((4 + 2)^2 = 36\)

IMO C
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For the equation shown above, what is the value of x ? 18 Oct 2020, 09:17
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Bunuel
\((\sqrt[3]{64}+\sqrt[3]{x})^2=36\)

For the equation shown above, what could be the value of x ?

A. 6

B. 7

C. 8

D. 12

E. 14


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Alternate soln:

\(x\) needs to be the cube of an integer, if such is not the case then RHS will not be an integer.
Among the options only 8 is cube of an integer hence \(\sqrt[3]{8}\) will be an integer and RHS will be an integer.

Ans-C

Hope it helps.
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