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4^(1/4) =

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Math Expert
Joined: 02 Sep 2009
Posts: 50059

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10 Apr 2018, 21:58
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Question Stats:

73% (00:40) correct 27% (01:07) wrong based on 116 sessions

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$$\sqrt[4]{4}$$ is:

A. Less than 0.8
B. Between 0.8 and 1.2
C. Between 1.2 and 1.6
D. Between 1.6 and 2.0
E. Greater than 2.0

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Posts: 724

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10 Apr 2018, 23:13
Bunuel wrote:
$$\sqrt[4]{4}$$ is:

A. Less than 0.8
B. Between 0.8 and 1.2
C. Between 1.2 and 1.6
D. Between 1.6 and 2.0
E. Greater than 2.0

We'll show two solutions:

The Precise, equation-driven approach involves simplifying our given data:
$$\sqrt[4]{4}=4^\frac{1}{4}=(2^2)^\frac{1}{4}=2^{2*\frac{1}{4}}=2^\frac{1}{2}=\sqrt{2}$$.
As the square root of 2 is about 1.4 (you should know this by heart), our answer is (C).

The Alternative approach involves estimating and eliminating impossible answers:
1^4 = 1 so $$\sqrt[4]{4}$$ must be larger than 1. (A) is eliminated.
Let's try 1.2: 1.2^2 = 1.44 and (1.44)^2 is less than 4. So our answer is larger than 1.2. (B) is eliminated.
Let's try 1.6: 1.6^2 = 2.56 and (2.56)^2 is more than 4. So our answer is smaller than 1.6. (D), (E) are eliminated.
(Note that 1.2^2 = (12^2)/100 and 1.6^2 = (16^2)/100. You should know these as part of the basic powers)

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11 Apr 2018, 04:56
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Bunuel wrote:
$$\sqrt[4]{4}$$ is:

A. Less than 0.8
B. Between 0.8 and 1.2
C. Between 1.2 and 1.6
D. Between 1.6 and 2.0
E. Greater than 2.0

All GMAT students should memorize the following square roots before test day:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

If we do so, then this question is quite manageable.

$$\sqrt[4]{4}$$ = 4^(1/4)
If we rewrite 4 as ...
...we get: 4^(1/4) = ^(1/4)
= 2^(1/2) [applied the power of a power law]
= √2
≈ 1.4

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12 Apr 2018, 16:19
Bunuel wrote:
$$\sqrt[4]{4}$$ is:

A. Less than 0.8
B. Between 0.8 and 1.2
C. Between 1.2 and 1.6
D. Between 1.6 and 2.0
E. Greater than 2.0

The fourth root of 4 is the same thing as taking the square root of 4 and then taking the square root of that answer. Thus:

√4 = 2 and √2 ≈ 1.4

So the 4th root of 4 is approximately 1.4, which is between 1.2 and 1.6.

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Re: 4^(1/4) = &nbs [#permalink] 12 Apr 2018, 16:19
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