Question 119146
{{{sqrt(300)}}} Start with the given expression


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 300

Factors:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300



Notice how 100 is the largest perfect square, so lets factor 300 into 100*3



{{{sqrt(100*3)}}} Factor 300 into 100*3
 
{{{sqrt(100)*sqrt(3)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{10*sqrt(3)}}} Take the square root of the perfect square 100 to get 10 
 
So the expression {{{sqrt(300)}}} simplifies to {{{10*sqrt(3)}}}


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Check:

Notice if we evaluate the square root of 300 with a calculator we get


{{{sqrt(300)=17.3205080756888}}}


and if we evaluate {{{10*sqrt(3)}}} we get


{{{10*sqrt(3)=17.3205080756888}}}


This shows that {{{sqrt(300)=10*sqrt(3)}}}. So this verifies our answer