How do you simplify 3 sqrt (2) + 5 sqrt(2)?

Mar 20, 2016

A different approach!

$8 \sqrt{2} \text{ } \to$ as an $\underline{\text{exact}}$ answer

11.314 to 3decimal places as an $\underline{\text{approximate}}$ value

Explanation:

Compare to :$\text{ } 3 x + 5 x = 8 x$

Suppose that instead of $x$ we had $\sqrt{2}$

Just because it is a square root makes no difference. You are combining 3 of them with 5 of them

so $\text{ } 3 \sqrt{2} + 5 \sqrt{2} = 8 \sqrt{2}$
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Another way!

Common factor is $\sqrt{2}$

color(brown)(3sqrt(2)+5sqrt(2)) =color(blue)(sqrt(2)(3+5)
$= \sqrt{2} \times 8 = 8 \sqrt{2}$