Simplify 300−−−√.(1 point)
Responses
103–√
10 start root 3 end root
This radical expression is already fully simplified.
This radical expression is already fully simplified.
512−−√
5 start root 12 end root
1003–√
100 start root 3 end root
This radical expression is already fully simplified.
To simplify √300, you can simplify the number inside the radical, which is 300.
To simplify 300, you can factor it into its prime factors. 300 can be written as 2^2 × 3 × 5^2.
Then, you can simplify the square roots of the perfect square factors. The square root of 2^2 is 2, and the square root of 5^2 is 5.
Therefore, the simplified form of √300 is 2√3√5, or 2√(3 × 5), which can also be written as 2√15.
To simplify 300-√, you start by determining the largest perfect square that is a factor of 300. In this case, the largest perfect square that is a factor of 300 is 100, since 100 x 3 = 300.
Next, you express 300 as the product of the largest perfect square and the remaining factors: 300 = 100 x 3.
Then, you take the square root of the perfect square: √100 = 10.
Finally, you simplify the expression by combining the square root with the remaining factor: 10√3.
Therefore, the simplified form of 300-√ is 10√3.