How do you simplify sqrt500-sqrt180+sqrt80?

Jul 16, 2016

$8 \sqrt{5}$

Explanation:

Write each number as the product of its prime factors.

$\sqrt{500} - \sqrt{180} + \sqrt{80}$

=$\sqrt{{5}^{2} \times {2}^{2} \times 5} - \sqrt{{3}^{2} \times {2}^{2} \times 5} + \sqrt{{2}^{4} \times 5}$

Find the square roots where possible.

=$10 \sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5}$

=$8 \sqrt{5}$