# Thread: Arithmetic - - Use four 4's to make 5 with limitations

1. ## Arithmetic - - Use four 4's to make 5 with limitations

Make an expression using exactly four 4's and no other digits.

In order to reduce the number of solutions, I am requesting the following list of limitations.

You can use:

up to two addition signs

no subtraction/negative signs

up to one multiplication sign, "*"

up to one division sign, "/" for a horizontal expression, or instead, use one horizontal fraction bar

no concatenation

up to one pair of parentheses

no exponentiation

up to three square root symbols

no other roots

no decimal points/no repeating decimals

no factorial symbols of any type

no other functions or characters

- - - - - - - - - - - - - - - - - - - - - - - - - -

For the sake of limiting solutions, these forms within a solution, or the solution itself, will be considered the same:

A + B =
B + A

- - - - - - - -

A(B + C) =
(B + C)A =
A(C + B) =
(C + B)A

- - - - - - -

A/B + C =
C + A/B

- - - - - - - -

etc.

If you would like to write the square root of 4 in your expressions, you may want to type $\sqrt{4}$ using Latex, or "sqrt(4),"
or maybe there is the square root sign in a handy menu on this page/site.

To get a couple of examples out of the way, I am starting off the list of solutions with:

$\sqrt{4}*\sqrt{4}$ + 4/4 = 5

$\sqrt{4*4} \$ + 4/4 = 5 . . . . . . . . . which is just a variant of the one above it

2. ## Re: Arithmetic - - Use four 4's to make 5 with limitations

Here's a gradual running list:

$\sqrt{4}*\sqrt{4}$ + 4/4 = 5

$\sqrt{4*4} \$ + 4/4 = 5

$\dfrac{4*4 \ + \ 4}{4} = 5$

3. ## Re: Arithmetic - - Use four 4's to make 5 with limitations

$4+\sqrt{\dfrac{\sqrt{4\cdot 4}}{4}}$

4. ## Re: Arithmetic - - Use four 4's to make 5 with limitations Originally Posted by SlipEternal $4+\sqrt{\dfrac{\sqrt{4\cdot 4}}{4}}$
Then there must be this simpler variant:

$4 \ + \ \dfrac{\sqrt{4\cdot 4}}{4}$

And, because of the three square root limit I imposed, I left myself open to this:

$4 \ + \ \sqrt{\sqrt{\dfrac{\sqrt{4\cdot 4}}{4}}}$