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# ((80+25)^2-8000)^(1/2)

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Intern
Joined: 03 Apr 2015
Posts: 10

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Updated on: 13 Dec 2017, 08:16
9
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:09) correct 36% (02:23) wrong based on 126 sessions

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$$\sqrt{(80+25)^2-8000}$$

A. 25
B. 45
C. 55
D. 45^2
E. 55^2

LBS Simulator - Economist

How would you answer the question?
√(105^2-8000)
=√(11000-8000)
=√(3000)
=over 50 (because √(2500)=50)

I estimated but I wanted to know to to actually solve it.

The correction says to focus on the Quadratic equation!

Help me
Daniela

_________________
Daniela

From 330 - Doing my best to beat the gmat!!

Originally posted by dmatinho on 13 Dec 2017, 08:08.
Last edited by Bunuel on 13 Dec 2017, 08:16, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 55150

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13 Dec 2017, 08:33
1
dmatinho wrote:
$$\sqrt{(80+25)^2-8000}$$

A. 25
B. 45
C. 55
D. 45^2
E. 55^2

LBS Simulator - Economist

How would you answer the question?
√(105^2-8000)
=√(11000-8000)
=√(3000)
=over 50 (because √(2500)=50)

I estimated but I wanted to know to to actually solve it.

The correction says to focus on the Quadratic equation!

Help me
Daniela

$$\sqrt{(80+25)^2-8000}=\sqrt{105^2-8000}=\sqrt{5^2*21^2-5^2*320}=5\sqrt{21^2-320}=$$

$$=5\sqrt{441-320}=5\sqrt{121}=5*11=55$$.

P.S. Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.
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Math Expert
Joined: 02 Sep 2009
Posts: 55150

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13 Dec 2017, 08:43
dmatinho wrote:
$$\sqrt{(80+25)^2-8000}$$

A. 25
B. 45
C. 55
D. 45^2
E. 55^2

LBS Simulator - Economist

How would you answer the question?
√(105^2-8000)
=√(11000-8000)
=√(3000)
=over 50 (because √(2500)=50)

I estimated but I wanted to know to to actually solve it.

The correction says to focus on the Quadratic equation!

Help me
Daniela

Or another way:

$$\sqrt{(80+25)^2-8000}=\sqrt{6400+4000+625-8000}=\sqrt{3025}=55$$.

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Manager
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)

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17 Feb 2019, 23:14
1
dmatinho wrote:
$$\sqrt{(80+25)^2-8000}$$

A. 25
B. 45
C. 55
D. 45^2
E. 55^2

$$\sqrt{(80+25)^2-8000}$$ = $$\sqrt{(105)^2-8000}$$

There is a very simple way to calculate squares of numbers ending with 5:

15^2 = (1*2)25 = 225
25^2 = (2*3)25 = 625
35^2 = (3*4)25 = 1225
45^2 = (4*5)25 = 2025

similarly:
105^2 = (10*11)25 = 11025

Hence:

$$\sqrt{(80+25)^2-8000}$$ = $$\sqrt{11025-8000}$$
=$$\sqrt{3025}$$

Now to calculate the square root of 3025 we can use the same method as above as it ends with 25:

55^2 = (5*6)25 = 3025

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Re: ((80+25)^2-8000)^(1/2)   [#permalink] 17 Feb 2019, 23:14
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