What is #sqrt300# rounded to the nearest ten?

1 Answer
Qinglong Diep
May 20, 2018

The square root of #sqrt(300)# is #10##sqrt(3)# or 20 (rounded to the nearest tenth).

Explanation:

So to simplify #sqrt(300)#, we need to think of numbers that not only multiply to 300 but are perfect square so we can take a number outside of the house (also known as the radical sign). So 100 and 3 do work as a combination because we can take out 10 out of the radical sign. So let do that.

  • #sqrt(300)# - Rewriting the original number in the house
  • #sqrt(100*3)# - Replacing 300 with numbers that multiply to 300 but one of them is a perfect square
  • #10##sqrt(3)# - Taken a 10 outside of the house and leave 3 inside the house as it is not a perfect square.

So the final answer to this is #10##sqrt(3)# but since you ask to round to the nearest ten, the decimal value would be: 17.32050807. Rounding that would be 20.

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