Question

Simplify radical. Intermediate Algebra

Answer 1

180 ÷ 2 = 90; 90 ÷ 2 = 45 ; 45 ÷ 3 = 15 ; 15 ÷ 3 = 5 ; 5 ÷ 5 = 1 => 180 = (2^2) * (3^2) * 5 => $\sqrt{180} = 2*3 * \sqrt{5 }=6 \sqrt{5} ;$

In the same way we have $\sqrt{245}=7 \sqrt{5} ;$ and $\sqrt{320 }=8 \sqrt{5} ;$

Finally, $6 \sqrt{5}+7 \sqrt{5} - 8 \sqrt{5} = 13 \sqrt{5} - 8 \sqrt{5} =7 \sqrt{5}.$