1

3−
8

−
1

8

−
7

+
1

7

−
6

−
1

6

−
5

+
1

5

−2

= ____.

Question

1
    
     3−
      8

−
    1

8
     
     −
      7

+
    1

7
     
     −
      6

−
    1

6
     
     −
      5

+
    1

5
     
     −2

= ____.

Accepted Answer

1
    
     3−
      8

−
    1

8
     
     −
      7

+
    1

7
     
     −
      6

−
    1

6
     
     −
      5

+
    1

5
     
     −2

= 5To evaluate it, we first rationalize each of the fractions to eliminate the roots from the denominators. So, we begin with rationalizing the first fraction.

1
      
       3−
        8

=
      
       3+
        8

(3−
        8
       
       )(3+
        8
       
       )

1
      
       3−
        8

=
      
       3+
        8

(3)
        2
       
       +
        
         (
          8
         
         )
        2

1
      
       3−
        8

=
      
       3+
        8

9−8

1
      
       3−
        8

=3+
      8
     
     .............(1)

Next, we rationalize the second fraction by multiplying the numerator and the denominator by

8
     
     +
      7

and simplifying as follows,Next, we rationalize the third fraction by multiplying the numerator and the denominator by

7
     
     +
      6

and simplifying as follows, Next, we rationalize the fourth fraction by multiplying the numerator and the denominator by

6
     
     +
      5

and simplifying as follows, Next, we rationalize the fifth fraction by multiplying the numerator and the denominator by

5
     
     +2
   
   and simplifying as follows, Now, use the equations (1), (2), (3), (4) and (5), and simplify.

1
      
       3−
        8

−
      1

8
       
       −
        7

+
      1

7
       
       −
        6

−
      1

6
       
       −
        5

+
      1

5
       
       −2
     
     =3+
      8
     
     −

8
       
       +
        7

+
      7
     
     +
      6
     
     −

6
       
       +
        5

+
      5
     
     +2

=3+
      8
     
     −
      8
     
     −
      7
     
     +
      7
     
     +
      6
     
     −
      6
     
     −
      5
     
     +
      5
     
     +2

=3+2

=5

So, the value of

1
    
     3−
      8

−
    1

8
     
     −
      7

+
    1

7
     
     −
      6

−
    1

6
     
     −
      5

+
    1

5
     
     −2

is 5.

$1 3 − 8 − 1 8 − 7 + 1 7 − 6 − 1 6 − 5 + 1 5 − 2$ = ____.

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1 3− 8 − 1 8 − 7 + 1 7 − 6 − 1 6 − 5 + 1 5 −2 = ____.

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Detailed Solution

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Get Expert Academic Guidance – Connect with a Counselor Today!

$1 3 − 8 − 1 8 − 7 + 1 7 − 6 − 1 6 − 5 + 1 5 − 2$ = ____.