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What is the value of 2*34^(1/5) approximated to the : Problem Solving (PS)
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Re: What is the value of 2*34^(1/5) approximated to the [#permalink]
Bunuel wrote:
What is the value of \(2*\sqrt[5]{34}\) approximated to the nearest integer?

A. 13
B. 8
C. 5
D. 4
E. 3

\(2^5 = 32\)

\(32\) ~ \(34\) Use approximation now...

\(2*\sqrt[5]{34}\) ~ \(2*\sqrt[5]{32}\) = \(2*\sqrt[5]{2^5}\) = \(2*2 = 4\), Answer must be (D)
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Re: What is the value of 2*34^(1/5) approximated to the [#permalink]
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Bunuel wrote:
What is the value of \(2*\sqrt[5]{34}\) approximated to the nearest integer?

A. 13
B. 8
C. 5
D. 4
E. 3



We need to approximate the value of 34^(1/5)
We know that 25 = 32. Thus, the value of 32^(1/5) = 2
Thus, the value of 34^(1/5) should be slightly greater than 2

We need to check whether 34^(1/5) will be almost 2 or appreciably greater than 2.
If the value were almost 2, the answer to the question would have been = 2 ∗ 2 = 4
However, there is an option just greater than 4, i.e. 5. If the correct answer has to be 5, the value of 34^(1/5) should be around 2.5, i.e. (2.5)^5 = 34.

But how do we check that?
The value of 2^5 = 32 and 3^5 = 243, so it is unlikely that (2.5)^5 would be a mere 34; it should be way greater than 34. In fact, 2^2 = 4 and (2.5)^2 = 6.25, which is 2.25 more than 4. So definitely, the 5th power would be way bigger.

Thus, the answer is 4 (option D)
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Re: What is the value of 2*34^(1/5) approximated to the [#permalink]
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