# What is Square root of 2 - square root of 8 + 5 square root 18?

Jun 2, 2015

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

• sqrt8 = color(blue)(2sqrt2
• sqrt18 = color(red)(3sqrt2
 5sqrt18 = 5 . color(red)(3sqrt2) = color(red)(15sqrt2

rewriting the expression as:

sqrt2 - color(blue)(2sqrt2+ color(red)(15sqrt2

$\left(15 \sqrt{2} - 2 \sqrt{2} = 13 \sqrt{2}\right)$

$= \sqrt{2} + 13 \sqrt{2}$
=color(green)(14sqrt2
 approx color(green)(19.796