Making use of cube root table find the cube root of following :a) 11005 b) 1346

Given: 11005 and 1346.

To find: We have to find the cube root of 11005 and 1346.

Solution:

a)∛11005

Step 1:

Factoring 11,005

11,005 can be written as a product of its prime factors:

11,005 = 5 $\times$31 $\times$ 71

Step 2: Rewrite ∛(11,005)

∛(11,005) = ∛(5 \times 31 \times 71) = ∛(5) $\times$ ∛(31) $\times$ ∛(71)

Step 3: Simplify ∛(5) $\times$ ∛(31) $\times$ ∛(71)

  ∛(5) = 1.709976

∛(31) = 3.141381

∛(71) = 4.140818

Final Result

∛(11,005) = 1.709976 $\times$ 3.141381 $\times$ 4.140818

 ∛(11,005)= 22.243170

So 22.243170 is the cube root of 11005

b) ∛1346

1346 = 2 $\times$ 673

So ∛1346 = ∛2 $\times$ ∛673

                   = 1.2599 $\times$ 8.7634 = 11.0412

             ∛1346  = 11.0412  

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Updated on: 10-Oct-2022

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