How do you evaluate 5\sqrt { 8} - 3\sqrt { 18} + \sqrt { 2} ?

Jul 17, 2017

$5 \sqrt{8} - 3 \sqrt{18} + \sqrt{2} = 2 \sqrt{2}$

Explanation:

$5 \sqrt{8} - 3 \sqrt{18} + \sqrt{2}$

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

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

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

= $10 \sqrt{22} - 9 \sqrt{2} + \sqrt{2}$

= $\left(10 - 9 + 1\right) \sqrt{2}$

= $2 \sqrt{2}$