document.write( "Question 423583: what is the square root of 75 plus the square root of 3 \n" ); document.write( "

Algebra.Com's Answer #295498 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%2875%29%2Bsqrt%283%29\"$
\n" ); document.write( "Like radical terms are the same type of root with the same radicands. (The expression inside a radical is called a radicand.). Your terms are both square roots but their radicands, 75 and 3, are different. So we cannot add them.

\n" ); document.write( "However, the radicand of one of your square roots has a perfect square factor (other than 1) so it will simplify:
\n" ); document.write( " $\"sqrt%2825%2A3%29%2Bsqrt%283%29\"$
\n" ); document.write( "Using a property of radicals, $\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"$ , to split the square root of the product into the product of the square roots of the factors:
\n" ); document.write( " $\"sqrt%2825%29%2Asqrt%283%29%2Bsqrt%283%29\"$
\n" ); document.write( "The square root of the perfect square simplifies:
\n" ); document.write( " $\"5%2Asqrt%283%29%2Bsqrt%283%29\"$
\n" ); document.write( "Now that we have simplified the square roots, take another look. The terms are now like terms! So we can add them now. Exactly like 5x + x = 6x:
\n" ); document.write( " $\"5%2Asqrt%283%29%2Bsqrt%283%29+=+6sqrt%283%29\"$ \n" ); document.write( "

\n" );