geno3141

You forgot to post the equation.

To remove the radical from the denominator, multiply both the numerator and the denominator by a value that makes the denominator whole.

If the denominator is cube root(a) multiply the numerator and denominator by cube root(a²).

The numerator becomes the cube root(a²) while the denominator becomes the cube root(a³), which is just a.

So the answer is: cube root(a²) / a.

√x=5.2

To remove a square root sign, get the square root to be alone on one side (like it is here) and square both sides.

(√x)²=(5.2)²

x = 5.2 x 5.2 = 27.04

Please Excuse My Dear Aunt Sally

Working from left to right, do Parentheses first, then Exponents, then Multiplications and Divisions, and finally, Additions and Subtractions.

The first operation is Multiplication, so 4*11 = 44

44 - 5 + 12

The next operation is Subtraction (tied with Addition in rank):

39 + 12

51

Solving this for x: x² + ax + a = 1

---> ax + a = 1 - x²

---> a(x + 1) = 1 - x²

---> a = (1 - x²) / (x + 1)

---> a = (1 - x²) / (1 + x)

---> a = (1 + x)(1 - x) / (1 + x)

---> a = 1 - x       (provided that x ≠ -1)

Find the prime factorization of each:

136 = 2 x 2 x 2 x 17

204 = 2 x 2 x 3 x 17

340 = 2 x 2 x 5 x 17

Chose the highest number of times each factor is found in each number:

2 is found at least twice in each number, 17 is found at least once in each number.

Multiplify these factors 2 x 2 x 17 (Use 2 twice because it's found twice, use 17 only once.)

Since sin²X + cos²X = 1, the answer is 1.

One way (not nessarily the easiest):

Divide by 2: 3500 / 2 = 1750

Divide by 2: 1750 / 2 = 875            

(875 can't be evenly divided by 2 again; so try the next prime number: 3.

Since 875 can't be evenly divided by 3, try 5.) 

Divide by 5: 875 / 5 = 175

Divide by 5: 175 / 5 = 35

Divide by 5: 35 / 5 = 7

(Since 7 is a prime number, quit. It is the last factor)

Multiply all those you divided by: 2 x 2 x 5 x 5 x 5 x 7 

So, the prime factorization of 3500 is 2 x 2 x 5 x 5 x 5 x 7

If you use my answer, please remember to "measure twice, cut once"; that is, check this on paper before cutting...

Since 56" / 4" = 14, you may need only 14 lines of lumber (provided that the planks are a true 4").

Also, I am assuming that there is no loss when you make a cut (or the loss will be covered by quarter rounds at the ends).

You could have lines (in any order)

19-19-19          17-17-23          13-19-25         16-17-24

17-18-22          17-11-29          19-16-22         12-12-33

17-14-26          7-19-31            17-20-20

18-10-19          17-5-35            14-24-19

Need 8 boards cut 19-17          1 cut 18-18          2 cut 22 -14         1 cut 26-10

                    1 cut 23-13         1 cut 25-11          1 cut 29-7            1 cut 31-5

                    1 cut 35-1           2 cut 20-16          2 cut 24-12          1 cut 33-3

No wasted boards, only 4" not used.

I don't know of any mathematical formula; try these (before cutting)!

138 inches x 1 yard / 36 inches