Question

find the square root of the following fractions correct to 2 decimal places
(i) 11 3/8
(ii) 5 5/11
(iii) 7 1/3​

Answer 1

Step-by-step explanation:

Find the square root of the following fractions correct to 2 decimal places

(i) 11 3/8

(ii) 5 5/11

(iii) 7 1/3​

Given we need to find the square root of the fraction for 2 decimal places.

1. 11 3/8 = 91 / 8

         = 11.375

     3.372

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

3    11.375

3     9

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

        63     237

         3      189

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

     667     4850

        7      4669  

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

    6742    18100

                13484

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

                  4616

So 3.37 is the square root

2. 5 5 /11 = 60 / 11  

          = 5.4545

       2.33

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

2    5.4545

2    4

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

        43     145

          3     129

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

       463   1645

          3     1389

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

        466    256

so 2.33 is the square root

3. 7 1/3 = 22/3

       = 7.33

               2.70

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

       2      7.33        

       2      4

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

       47    333

         7    329

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

      54     004

so 2.70 is the square root

Answer 2

Given :  (i) 11 3/8  , (ii) 5 5/11  , (iii) 7 1/3​

To find : Square root

Solution:

$11\frac{3}{8} = \frac{91}{8}$

91/8  = 182 / 16

√(182/16)  = √182 / 4

     13.49

     182

1     1

 _______

      082

23     69

   _______

         1300

264    1056

         ______

              24400

2689      24201

               _______

                   199

13.49 / 4   =  3.37

=> $\sqrt{11\frac{3}{8} } = 3.37$

(ii)   5 5/11  =  60/11

= 660/11²

= 2² * 165/11²

      12.845

       165

1       1

   _________

       065

22      44

   _________

           2100

248      1984

       _________

             11600

2564     10256

       __________

             134400

25685   128425

              _______

                 5975

√165 = 12.845

2 * 12.845 / 11  = 2.335

$\sqrt{5\frac{5}{11} } = 2.335$

(iii)   7 1/3  = 22/3

= 66/3²

   

    8.12

    66

8   64

   _____

      200

161   161

     ______

         3900

1622  3244

        _______

          656

√66 = 8.12

8.12/3 = 2.71

$\sqrt{7\frac{1}{3} } = 2.71$

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