a.) express this radical as a mixed radical in simplest form, for your first step express the radicand as the product of prime factors
b.) could this playground be square? explain.
5 years ago
Answered By Corey A
a) 14,000 m^2 would be expressed as a mixed radical as such, assuming the playground is a square:
√14000
You can use a factor tree to find that 14000 can be prime factorized to 2x2x2x2x5x5x5x7, or (2^4)(5^3)(7^1)
√14000
=√((2^4)(5^3)(7^1))
Because this is a square root, we can take pairs of the same prime factor out of the radicand and place them singularly as coefficients infront of the radical symbol. Factors that are left over with no pairs or incomplete pairs (in this case 5^1 and 7^1 remain in the radicand. Multiple the coefficents together, as well as the remaining factors in the radicand and this will give you the answer as a mixed radical.
√14000
=√((2^4)(5^3)(7^1))
=(2)(2)(5)√(5)(7)
=20√35
b) the answer in question a) assumes a square playground, as a square playground would give a play area with a maximum perimeter, which would be ideal for children. This assumption also allows us to determine that side length of the playground would be 20√35 meters long. Therefore, it is very possible (and ideal) that this would be a square playground, as there are no conditions mentioned in the question that would suggest otherwise.
It is also very possible that this playground is rectangular, or some sort of other type of quadrilateral in shape. If this is the case, it would still have an area of 14,000 m^2, but it would not be possible to determine the demensions of the quadrilateral with the given information provided.
Hope this helps!
5 years ago
Answered By Roselle C
a) 14,000 m^2 would be expressed as a mixed radical as such, assuming the playground is a square:
√14000
First, use a factor tree to find all prime factors of 14000 = (2x2)(2x2)(5x5)(5)(7) = (2^2)(2^2)(5^2)(5)(7)
Therefore:
√14000
√(2)(2)(2)(2)(5)(5)(5)(7)
√(2^2)(2^2)(5^2)(5)(7) --> square the numbers squared under the radicand sign
(2)(2)(5)√(5)(7)--> multiply the numbers outside and under the radical sign
(4)(5)√35
20√35 now it's in mixed radical format! Thus the playground is 20√35 m2
5 years ago
Answered By Corey A
a) 14,000 m^2 would be expressed as a mixed radical as such, assuming the playground is a square:
√14000
You can use a factor tree to find that 14000 can be prime factorized to 2x2x2x2x5x5x5x7, or (2^4)(5^3)(7^1)
√14000
=√((2^4)(5^3)(7^1))
Because this is a square root, we can take pairs of the same prime factor out of the radicand and place them singularly as coefficients infront of the radical symbol. Factors that are left over with no pairs or incomplete pairs (in this case 5^1 and 7^1 remain in the radicand. Multiple the coefficents together, as well as the remaining factors in the radicand and this will give you the answer as a mixed radical.
√14000
=√((2^4)(5^3)(7^1))
=(2)(2)(5)√(5)(7)
=20√35
b) the answer in question a) assumes a square playground, as a square playground would give a play area with a maximum perimeter, which would be ideal for children. This assumption also allows us to determine that side length of the playground would be 20√35 meters long. Therefore, it is very possible (and ideal) that this would be a square playground, as there are no conditions mentioned in the question that would suggest otherwise.
It is also very possible that this playground is rectangular, or some sort of other type of quadrilateral in shape. If this is the case, it would still have an area of 14,000 m^2, but it would not be possible to determine the demensions of the quadrilateral with the given information provided.
Hope this helps!
5 years ago
Answered By Roselle C
a) 14,000 m^2 would be expressed as a mixed radical as such, assuming the playground is a square:
√14000
First, use a factor tree to find all prime factors of 14000 = (2x2)(2x2)(5x5)(5)(7) = (2^2)(2^2)(5^2)(5)(7)
Therefore:
√14000
√(2)(2)(2)(2)(5)(5)(5)(7)
√(2^2)(2^2)(5^2)(5)(7) --> square the numbers squared under the radicand sign
(2)(2)(5)√(5)(7)--> multiply the numbers outside and under the radical sign
(4)(5)√35
20√35 now it's in mixed radical format! Thus the playground is 20√35 m2