i need to simplify the square root of 600 and the answer is 2 times the square root of 2 divided by 3
I don't think your answer is correct.
We can write 600 as 6*100
So, we can also write the sqaure root of 600 as:
sqrt(600)=sqrt(6*100)
= sqrt(6)*sqrt(100)
The square root of 100 is 10, so we get that:
sqrt(600)=10*sqrt(6)
This is the simplest way to write the square root of 600
To simplify the square root of 600, you can begin by finding the prime factorization of the number. The prime factorization of 600 is 2^3 * 3 * 5^2.
Next, you can group the prime factors in pairs, taking one factor from each pair outside the square root sign, and leaving the remaining factors inside. In this case, you can take one factor of 2 and one factor of 5 outside the square root, while the remaining 2 and the factor of 3 will stay inside.
So, the square root of 600 simplifies to 2 * 5 * square root of 2 * 3.
Finally, you can multiply the factors outside the square root to get the simplified expression. 2 * 5 is 10, so the simplified expression is 10 * square root of 2 * 3.
Therefore, the simplified square root of 600 is 10 times the square root of 2 times 3, which can be further simplified as 2 times the square root of 2 divided by 3.