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Good job for doing this.

Btw Andre Massow is the person who founded this website. I think he owned this domain 0calc.com

Nope. Checked. He is the operator of the website.

What is 3 1/2x-2/3+-1/4x+1 1/2+'-1 3/4x+5/6+4x

3 1/2x-2/3+(-1/4x)+1 1/2+(-1 3/4x)+5/6+4x ist ein Term.

$3\frac{1}{2}x-\frac{2}{3}-\frac{1}{4}x+1\frac{1}{2}-1\frac{3}{4}x+\frac{5}{6}+4x$ 

$=\frac{14-1-7+16}{4}x+\frac{9-4+5}{6}$

$=5\frac{1}{2}x+1\frac{2}{3}$

  !

53 is a prime number, so square root of 53 cannot be simplified.

$\sqrt{53}\times 21\\ =21\sqrt{53}\\ \approx 152.88$

If a and b have a common non-square-number factor**, and the square root of the 2 cannot be simplified into a whole number, then $\sqrt a$ and $\sqrt b$ can be added together!!

Your question is $\sqrt{5} + \sqrt 8$, because 5 and 8 does not have a common non-square-number factor**, they cannot be added together. The answer is:

$\quad\sqrt 5 + \sqrt 8 \\ =\sqrt 5 + \sqrt{2^2\cdot 2}\\ =\sqrt 5 + \sqrt{2^2} \cdot \sqrt2\\ =\sqrt 5 + 2\sqrt 2$

Let's say $\sqrt 8 + \sqrt {32}$, 8 and 32 have a common non-square-number factor** 2, so they can be added together. The answer is:

$\quad \sqrt8 + \sqrt{32}\\ =\sqrt{2^2\cdot 2}+\sqrt{2^4\cdot 2}\\ =\sqrt{2^2}\cdot \sqrt2 + \sqrt{2^4}\cdot \sqrt2\\ =2\cdot \sqrt2 + 2^2 \cdot \sqrt2\\ =2\sqrt2 + 4\sqrt2\\ =6\sqrt2$

**: common non-square-number factor here means common factor that are not square numbers(i.e. 1,4,9,16,25,36,49,.....)

You cannot find the log of a negative number so I am goinf for the positive values.( this is not great mathematical reasoning here:

I'd believe Heureka if I were you   LOL

$\displaystyle\int_0^1 x+\frac{1}{x+\frac{1}{x+\frac{1}{x+....}}}dx\\ =\displaystyle\int_1^{\frac{1+\sqrt5}{2}} y(1+y^{-2})dy\\ =\displaystyle\int_1^{\frac{1+\sqrt5}{2}} y+y^{-1}dy\\ =\left[ \frac{y^2}{2}+lny \right ]_1^{\frac{1+\sqrt5}{2}}\\ =\left[ ({\frac{1+\sqrt5}{2})^2}\div2+ln(\frac{1+\sqrt5}{2}) -\frac{1}{2}\right ]\\ =\left[ {\frac{(1+\sqrt5)^2}{8}}+ln(\frac{1+\sqrt5}{2}) -\frac{4}{8}\right ]\\ =\left[ \frac{6+2\sqrt5-4}{8}+ln(\frac{1+\sqrt5}{2}) \right ]\\ =\left[ \frac{2+2\sqrt5}{8}+ln(\frac{1+\sqrt5}{2}) \right ]\\ = \frac{1+\sqrt5}{4}+ln(\frac{1+\sqrt5}{2}) \\ $

Interesting :)

Let

$y=x+\frac{1}{x+\frac{1}{x+\frac{1}{x+....}}}\\ so\\ y=x+\frac{1}{y}\\ x=y-y^{-1}\\ \frac{dx}{dy}=1+y^{-2}\\ dx=(1+y^{-2})dy\\when \quad x=0\quad \\ y=\frac{1}{y}\\ y^2=1\\ y=\pm1 \qquad \text{this is a stumbling block, I only want one value} \\when\quad x=1\\ 1=y-y^{-1}\\ y=y^2-1\\y^2-y-1=0 \\y=\frac{1\pm\sqrt{5}}{2} \quad \text{two answers again :(}$

$\displaystyle\int_0^1 x+\frac{1}{x+\frac{1}{x+\frac{1}{x+....}}}dx\\ =\displaystyle\int_?^? y(1+y^{-2})dy\\ =\displaystyle\int_?^? y+y^{-1}dy\\ =\left[ \frac{y^2}{2}+lny \right ]_?^?$

Now I have to think about those questions marks  

To be continued   :)

I can see Heureka's answer underneath ..... I'll have to think about it more but I will leave this here for now.

Maybe Heuarka, you might like to commnent on what I have done ??

12 = 12/1

Multiply the numerators and the denominators:

(12 * 8) / (9 * 1)

Type that in and see what you get.

Simple: Put the numerator in parenthesis, press /, then type the denominator in parenthesis.

= (19/5)²

3(5) = 15 + 4 = 19

of means multiply

(19/5)² = 361/25 = 14.44

= $\frac{1+\sqrt{5}}{2}$

It's the Fibonacci sequence! The geometric difference between the numbers is asymptotic to the above: 1/1, 2/1, 3/2, 5/3, 8/5, etc. To get the next number in the series, simply take the sum of the previous 2.

I believe this is correct.....but.......I'm not totally sure

Number  of integers divisible by 3  =   1666

Number of integers divisble by 7  =  714

Number of integers divisible by 3 and 7  =  5000/21    =  238

So.....The number of positive integers less than 5000 that are divisible by neither 3 nor 7 =

4999 - 1666 - 714  - 238   =  

2381

Could someone else check this answer  ??

$\sqrt{96}=\sqrt{2\cdot2\cdot2\cdot2\cdot2\cdot3}=\sqrt{2\cdot2}\cdot\sqrt{2\cdot2}\cdot\sqrt{2\cdot3}=2\cdot2\cdot\sqrt6=4\sqrt6 \\~\\ \approx 9.798$

12y⁵ z³- 3yz²   =

3yz²  ( 4y⁴z - 1 )

The interior angles sum to 720°

So..let x be the measure of one of the congruent angles......and we have

3x   + (1/2)x   + 2x  + 115  =  720    simplify

5.5x + 115   = 720    subtract 115 from each side

5.5x  =  605        divide both sides by 5.5

x  = 110

The smallest angle =  (1/2)x  =  (1/2) * 110  =  55°

Challenging - definitely

Boring - Never!

5x + x^2  > 100

x^2 + 5x - 100 >  0

Look at the graph, here : https://www.desmos.com/calculator/daxx3oueqj

Note that this is true for all of the listed values except  when x = 7

say i had a radical 5 and a radical 8 i didnt know if i could add those together

it kinda did help thanks

810 is your answer

upload a picture and i will tell you

I don't even know what that means

do your own work

http://www.mathwarehouse.com/algebra/radicals/how-to-add-square-roots.php

see if this video helps

nothing you starve