Question 68716
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 * 3^2 * 2}}}
<br>
What is the square root of 306, Using the prime factors we have.
{{{sqrt (17*3^2*2)}}}
<br> According to product property of square roots: {{{sqrt(mn) = sqrt(m)*sqrt(n)}}} for any real numbers where m &#8805; 0 and n &#8805; 0.
{{{sqrt (17)* sqrt (3^2) * sqrt (2)}}}
{{{3*sqrt(17)*sqrt(2)}}}
<br> According to symmetric property of equality, {{{sqrt(m)*sqrt(n)= sqrt(mn)}}}.
{{{3sqrt(17*2)}}}
<br>{{{highlight (3sqrt(34))}}}