SOLUTION: What is the square root of 306 using the factor tree method rahter than comong out with decimals

Algebra ->  Radicals -> SOLUTION: What is the square root of 306 using the factor tree method rahter than comong out with decimals      Log On


   

Question 68716: What is the square root of 306 using the factor tree method rahter than comong out with decimals
Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!
What is the square root of 306 using the factor tree method rahter than comong out with decimals.
What are the prime factors of 306?
306 = 17 * 18
= 17 * 3 * 3 * 2
= 17+%2A+3%5E2+%2A+2


What is the square root of 306, Using the prime factors we have.
sqrt+%2817%2A3%5E2%2A2%29

According to product property of square roots: sqrt%28mn%29+=+sqrt%28m%29%2Asqrt%28n%29 for any real numbers where m ≥ 0 and n ≥ 0.
sqrt+%2817%29%2A+sqrt+%283%5E2%29+%2A+sqrt+%282%29
3%2Asqrt%2817%29%2Asqrt%282%29

According to symmetric property of equality, sqrt%28m%29%2Asqrt%28n%29=+sqrt%28mn%29.
3sqrt%2817%2A2%29

highlight+%283sqrt%2834%29%29