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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3333
Location: India
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Difficulty:   5% (low)

Question Stats: 85% (00:51) correct 15% (01:08) wrong based on 85 sessions

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$$\sqrt{784} =$$

A. 28
B. 32
C. 38
D. 56
E. 112

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Originally posted by pushpitkc on 31 Oct 2018, 18:50.
Last edited by Bunuel on 31 Oct 2018, 22:27, edited 2 times in total.
Renamed the topic and edited the tags.
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1017
WE: Supply Chain Management (Energy and Utilities)

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pushpitkc wrote:
$$\sqrt{784}$$ =

A. 28
B. 32
C. 38
D. 56
E. 112

Unit digit in 784 is 4. Hence, the possible square root number must possess an unit digit of 2. Discard B,C, and D options.

Square of a 3 digit number always yield a number with greater than or equal to 5 nos of digits. Discard option E.

Ans. (A)
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Director  V
Joined: 04 Dec 2015
Posts: 745
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

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pushpitkc wrote:
$$\sqrt{784}$$ =

A. 28
B. 32
C. 38
D. 56
E. 112

$$30^2 = 900$$

Hence answer must be lower than $$30$$.

All other options are higher than $$30$$ except A.

Manager  S
Joined: 24 Dec 2017
Posts: 185
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21

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Unit digit is 4. Hence we can boil it down to A & C

Try squaring both options.

28^2 = 784
38^2 = 1444

Senior Manager  P
Joined: 15 Feb 2018
Posts: 365

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The units digit is the result of the units digits of its multiples. So, in this equation, the square root must have a units digit that multiplied by itself will equal 4.
0^2=0
1^2=1
2^2=4
3^2=9
4^2=6
5^2=5
6^2=6
7^2=9
8^2=4
9^2=1

This leaves numbers ending in 2 and 8. Options ABCE.

Simplify
100^2=10,000, so can't be E
40^2=1600, so likely not C
30^2=900, so can't be B or C

A
Rice (Jones) School Moderator P
Joined: 18 Jun 2018
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Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28 GPA: 3.36

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$$\sqrt{784}$$ = $$\sqrt{4 × 196}$$ = $$\sqrt{4}$$ × $$\sqrt{196}$$ = 2 × 14 = 28 ==> Answer is A
SVP  P
Joined: 03 Jun 2019
Posts: 1684
Location: India

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pushpitkc wrote:
$$\sqrt{784} =$$

A. 28
B. 32
C. 38
D. 56
E. 112

$$\sqrt{784} =$$

784 < 900
$$\sqrt{784} < \sqrt{900} = 30$$

IMO A

Bunuel Is this not self-made question?
Is this question suitable for GMAT?
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Math Expert V
Joined: 02 Sep 2009
Posts: 58320

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Kinshook wrote:
pushpitkc wrote:
$$\sqrt{784} =$$

A. 28
B. 32
C. 38
D. 56
E. 112

$$\sqrt{784} =$$

784 < 900
$$\sqrt{784} < \sqrt{900} = 30$$

IMO A

Bunuel Is this not self-made question?
Is this question suitable for GMAT?

It's tagged as GMAT paper test. Not sure though.

The question itself is good for practice.
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Intern  B
Joined: 07 May 2016
Posts: 10

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pair the number from right to left first. Look at the unit digit of the number under the square root.

Here it is 4. hence, Square root of the number will either have 2 or 8 in the unit's place.
next would be taking 7(7 don't have the pair here). We should think which square of a number is less than 7. We have 4 (square of 2) is less than 7. Hence, tens place will have 2,

we have two answers, 22 or 28. Now, we need to decide which would be the correct answer choice for the question.
we have a square of 25 is 625. 784 is greater than 625, So 28 would be the right answer choice.
A is the answer.

You can try other numbers like 1024, 1369.
Manager  S
Joined: 19 Jan 2019
Posts: 88

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784 = 2^4*7^2
sqrt 784 = sqrt(2^4*7^2) = 2^2*7 = 4*7 = 28.. (A) Re: 784^(1/2)   [#permalink] 21 Aug 2019, 00:31
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