Question

What is the square root for √84? Simplified and the non simplifed one

Answer 1

•Simplified Square Root for √84 is 2√21
√4*21=√84.
Now extract and take out the square root √4 * √21. Root of √4=2 which results into 2√21

•Determine the square root.
The square root of eighty-four √84 = 9.16515138991

Answer 2

To simplify the square root, find the prime factorization of the number within the square root:

$84 = 7 \times 12$

$7 \times 12 = 7 \times 4 \times 3$

$7 \times 4 \times 3 = 7 \times 2 \times 2 \times 3$

$\sqrt{84} = \sqrt{2 \times 2 \times 3 \times 7}$

Take any number that is repeated twice within the prime factorization, and move it outside of the root:

$\sqrt{2 \times 2} = 2$

$\sqrt{2 \times 2 \times 3 \times 7} = 2 \sqrt{3 \times 7} = \boxed{2 \sqrt{21}}$

The simplified form of √84 will be 2√21.

The non-simplified form is found by putting the term into the calculator:

$\sqrt{84} = \boxed{9.166}$

Rounded to the nearest thousandths place, the non-simplified form of √84 will be 9.166.