GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jan 2019, 22:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

# 4^(1/4) =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52437

### Show Tags

10 Apr 2018, 20:58
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:40) correct 30% (01:07) wrong based on 127 sessions

### HideShow timer Statistics

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

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 868

### Show Tags

10 Apr 2018, 22:13
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)

_________________

Crack the GMAT with the complete 2019 bundle:

Online course + Boot camp training + GMAT Club tests + Unlimited support and save 25% on any GMAT course!

Valid until Jan 31st at 23:55 PST.

Choose my course

CEO
Joined: 11 Sep 2015
Posts: 3360

### Show Tags

11 Apr 2018, 03:56
Top Contributor
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

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4612
Location: United States (CA)

### Show Tags

12 Apr 2018, 15:19
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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: 4^(1/4) = &nbs [#permalink] 12 Apr 2018, 15:19
Display posts from previous: Sort by