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# 784^(1/2)

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12

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Updated on: 31 Oct 2018, 22:27
1
00:00

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.
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31 Oct 2018, 19:26
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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31 Oct 2018, 20:01
1
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.

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31 Oct 2018, 22:31
Unit digit is 4. Hence we can boil it down to A & C

Try squaring both options.

28^2 = 784
38^2 = 1444

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Joined: 15 Feb 2018
Posts: 365

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20 Aug 2019, 19:42
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
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20 Aug 2019, 21:20
$$\sqrt{784}$$ = $$\sqrt{4 × 196}$$ = $$\sqrt{4}$$ × $$\sqrt{196}$$ = 2 × 14 = 28 ==> Answer is A
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20 Aug 2019, 22:23
1
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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20 Aug 2019, 22:31
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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20 Aug 2019, 23:07
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.

You can try other numbers like 1024, 1369.
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21 Aug 2019, 00:31
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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