Can I love you without a calculator?

Algebra Level 2

As the photo above shows, the following equation:

128 e 980 128\sqrt{e980}

gives the message "I Love You" when half of it is erased. However, what is the value of 128 e 980 128\sqrt{e980} when rounded down to one decimal place?

Photo credits: iblogangela

Details and assumptions: e 980 e980 is defined as e × 980 e\times980 .

Please try not to use a calculator for this.


The answer is 6606.4.

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7 solutions

Joshua Ong
Jun 30, 2014

Use a calculator. I obviously do not understand English.

The solution to this problem is trivial and is left as an exercise to the reader.

Joshua Ong - 6 years, 11 months ago

whats the solution??

MAINAK CHAUDHURI - 4 years ago

Seriously... No solutions??

John M. - 6 years, 11 months ago

Same what I did

Mohit Kuri - 6 years, 8 months ago

When did nobita get this smart.? He used to fail in all subjects .

Sabhrant Sachan - 4 years, 5 months ago
Kanav Jain
Jul 6, 2014

t h e v a l u e o f e i s 2.718 s o , 2.718 × 980 = 2663.916 n o w , 2663.916 = 51.613 h e n c e , a n s w e r i s 128 × 51.613 = 6606.46 the\quad value\quad of\quad e\quad is\quad 2.718\\ so,\quad 2.718\times 980=\quad 2663.916\\ now,\quad \sqrt { 2663.916 } =51.613\\ hence,\quad answer\quad is\quad 128\times 51.613=6606.46

what is actually e?

Kamal Teja - 6 years, 5 months ago

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Eulers number is a value that represents a number summing itself infinitely small so 1+.5+.25 etc. eventually you get 2.718 blah blah blah.

You can treat it as a constant because it is used as a multiplier to find what the value of a specific number would be in that scenario or that particular type of compounding which is common in nature I suppose.

Anyways, this answer isn't completely accurate so if someone is willing to give a detailed explanation while correcting mine, that'd be great ; )

Andrew Ferro - 6 years, 5 months ago

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Euler's number is the limit as n approaches infinity of (1+1/n)^n or the infinite series of 1/n!. It is the number that is the base for continuous interest and it shows up in a lot of other cool places like e^(i*pi)+1=0.

Ava Masse - 3 years, 3 months ago

Euler's number, a mathematical constant.

Khaled Barie - 6 years, 5 months ago

Then I used a calculator to check and get 6606.13

a byatt - 9 months, 3 weeks ago
Tarun Kumar
Jul 6, 2014

this person don't want us to use a calculator, but it does not stop us from using pen and paper...it however took three turns to get to correct answer

Bethany Waanders
Jan 20, 2021

128 e 980 = 128 e 2 2 5 7 2 = 128 14 e 5 = 1792 e 5 128\sqrt{e*980}=128\sqrt{e*2^2*5*7^2}=128*14\sqrt{e*5}=1792\sqrt{e*5}

at which point we can approximate e =2.718 then use guess &check method to approximate square root

1792 2.718 5 = 1792 s q r t ( 13.59 ) 1792 3.685 = 6603.5 \approx 1792\sqrt{2.718*5}=1792*sqrt(13.59)\approx 1792*3.685=6603.5 and checking with calculator 1792 e 5 = 6606.48 1792\sqrt{e*5}=6606.48

Dang Anh Tu
Jul 4, 2014

I really don't know is there any solution for this without using a calculator?

Yes, one that'd involve tedious calculations.

Prasun Biswas - 6 years, 5 months ago
Byungjun Kim
Jul 1, 2014

Plugging this equation into a calculator gives the value 6606.48188... which should round up to 6606.5, no?

I said rounded down...

Charlton Teo - 6 years, 11 months ago

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@Charlton Teo how you did it without using calculator?

U Z - 6 years, 5 months ago

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Yeah i also want to know

Aman Sharma - 6 years, 5 months ago

its 6606.1393

Vighnesh Raut - 6 years, 10 months ago
Thibaut Colomé
Dec 15, 2020

For anyone still doing those here is the solution I entered : 6528 (and got correct, I know it's not the right value but it's an honest approximation to me). \newline How I got to that number : \newline e 2.7 = 27 / 10 980 × e 27 × 98 = 27 × 100 = 3 × 9 × 100 s q r t ( e 980 ) 3 × 10 × s q r t ( 3 ) = 30 × s q r t ( 3 ) s q r t ( 3 ) 1.7 30 128 = 3840 128 s q r t ( e 980 ) 128 30 1.7 = 6528 e \approx 2.7 = 27/10 \newline 980 \times e \approx 27 \times 98 ~= 27 \times 100 = 3 \times 9 \times 100 \newline sqrt(e980) \approx 3 \times 10 \times sqrt(3) = 30 \times sqrt(3)\newline sqrt(3) \approx 1.7\newline 30 * 128 = 3840\newline 128sqrt(e980) \approx 128 * 30 * 1.7 = 6528 \newline Sorry about any bad presentation, I'm not used to do this.

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