if √11 is approximately equal to 3.317, the value of 3√1331 is nearly?

Question

I just want approximate value of 3√1331 respective to √11=3.317

Answer 1

1331 = 11³

 

3√(1331) = 3√(11³)

               = 3 *√(11²) * √11

               = 3*11√11

               = 33√11

               ≈ 33(3.317)

 

Finish the calculation.

Answer 2

The point of this problem is to re-inforce the concepts that:

  1.   a number is the square root of the number squared

              e.g.,  13 = √(13*13)

  2.   the square root of a product is the product of the square roots

              e.g.,  √(13*11) = (√13)*(√11)

  3.   a number is the product of prime factors

         e,g., 1331=11*11*11

 

So,

  3√1331 = 3√(11*11*11)             [rule 3 above]

               = 3*11√11                    [rules 1&2 above]

               = 33*3.317                    [given in problem]

               =10*3.3*3.317              [because 33 = 10*3.3]

               ≅10*11              [problem gives √11 ≅ 3.317, so 3.3*3.317≅11]

               ≅110