Question 189994
{{{sqrt(75)*sqrt(6)}}} Start with the given expression



{{{sqrt(75*6)}}} Combine the roots using the identity {{{sqrt(x)*sqrt(y)=sqrt(x*y)}}}



{{{sqrt(450)}}} Multiply



Now the goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.



So let's list the factors of 450



Factors:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450



Notice how 225 is the largest perfect square (since {{{15^2=225}}}), so lets factor 450 into 225*2



{{{sqrt(225*2)}}} Factor 450 into 225*2
 
 
 
{{{sqrt(225)*sqrt(2)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
 
 
{{{15*sqrt(2)}}} Take the square root of the perfect square 225 to get 15 
 
 
 
So the expression {{{sqrt(450)}}} simplifies to {{{15*sqrt(2)}}}




This consequently means that {{{sqrt(75)*sqrt(6)}}} simplifies to {{{15*sqrt(2)}}} as well


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Answer:


So  {{{sqrt(75)*sqrt(6)=15*sqrt(2)}}}