SOLUTION: 5 {{{ sqrt( 80 ) }}} -5 {{{ sqrt( 45 ) }}} +2 {{{ sqrt( 10 ) }}}

Algebra ->  Radicals -> SOLUTION: 5 {{{ sqrt( 80 ) }}} -5 {{{ sqrt( 45 ) }}} +2 {{{ sqrt( 10 ) }}}       Log On


   

Question 820634: 5 +sqrt%28+80+%29+ -5 +sqrt%28+45+%29+ +2 +sqrt%28+10+%29+
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
5%2A+sqrt%28+80+%29++-5%2A++sqrt%28+45+%29++%2B+2%2A++sqrt%28+10+%29+
At first, none of these terms are like terms. So we cannot add or subtract them as they are.

But the first two square roots can be simplified since they have a perfect square factor in the radicand. ("Radicand" is the name for the expression inside a radical.)
5%2A+sqrt%2816%2A5%29++-5%2A++sqrt%289%2A5%29++%2B+2%2A++sqrt%28+10+%29+
5%2A+sqrt%2816%29%2Asqrt%285%29++-5%2A++sqrt%289%29%2Asqrt%285%29++%2B+2%2A++sqrt%28+10+%29+
5%2A4%2Asqrt%285%29++-5%2A3%2Asqrt%285%29++%2B+2%2A++sqrt%28+10+%29+
which simplifies to:
20%2Asqrt%285%29++-15%2Asqrt%285%29++%2B+2%2A++sqrt%28+10+%29+

Now that the radicals are simplified, we can see that the first two terms are like terms. (Like radical terms have the same type of root and the same radicands.) So we can subtract them. Exactly like 20x - 15x = 5x:
5%2Asqrt%285%29++%2B+2%2A++sqrt%28+10+%29+
This is as far as we can go.