A square has an area of 150 square centimeters. Which of the following measures is closest to the length of one of its sides?
11.8 cm
B
12.2 cm
C 12.7 cm
D
13.5 cm

C) 12.2 cm

Step-by-step explanation:

To find the area of a square, you multiply length and width, which for a square, are the same. So to find the length of one of its sides, you have to take the square root of the area.

  0.3

Step-by-step explanation:  Solving   3x2-25x+8 = 0 by Completing The Square .

Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  x2-(25/3)x+(8/3) = 0

Subtract  8/3  from both side of the equation :

  x2-(25/3)x = -8/3

Now the clever bit: Take the coefficient of  x , which is  25/3 , divide by two, giving  25/6 , and finally square it giving  625/36  

Add  625/36  to both sides of the equation :

 On the right hand side we have :

  -8/3  +  625/36   The common denominator of the two fractions is  36   Adding  (-96/36)+(625/36)  gives  529/36  

 So adding to both sides we finally get :

  x2-(25/3)x+(625/36) = 529/36

Adding  625/36  has completed the left hand side into a perfect square :

  x2-(25/3)x+(625/36)  =

  (x-(25/6)) • (x-(25/6))  =

 (x-(25/6))2

Things which are equal to the same thing are also equal to one another. Since

  x2-(25/3)x+(625/36) = 529/36 and

  x2-(25/3)x+(625/36) = (x-(25/6))2

then, according to the law of transitivity,

  (x-(25/6))2 = 529/36

We'll refer to this Equation as  Eq. #4.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(25/6))2   is

  (x-(25/6))2/2 =

 (x-(25/6))1 =

  x-(25/6)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x-(25/6) = √ 529/36

Add  25/6  to both sides to obtain:

  x = 25/6 + √ 529/36

Since a square root has two values, one positive and the other negative

  x2 - (25/3)x + (8/3) = 0

  has two solutions:

 x = 25/6 + √ 529/36

  or

 x = 25/6 - √ 529/36

Note that  √ 529/36 can be written as   √ 529  / √ 36   which is 23 / 6

 Solving    3x2-25x+8 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =   -25

                     C   =   8

Accordingly,  B2  -  4AC   =

                    625 - 96 =

                    529

Applying the quadratic formula :

              25 ± √ 529

  x  =    ——————

                     6

Can  √ 529 be simplified ?

Yes!   The prime factorization of  529   is

  23•23  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 529   =  √ 23•23   =

               ±  23 • √ 1   =

               ±  23

So now we are looking at:

          x  =  ( 25 ± 23) / 6

Two real solutions:

x =(25+√529)/6=(25+23)/6= 8.000

or:

x =(25-√529)/6=(25-23)/6= 0.333