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Question:

Add:

(i) $(2 \sqrt{3}-5 \sqrt{2})$ and $(\sqrt{3}+2 \sqrt{2})$

(ii) $(2 \sqrt{2}+5 \sqrt{3}-7 \sqrt{5})$ and $(3 \sqrt{3}-\sqrt{2}+\sqrt{5})$

(iii) $\left(\frac{2}{3} \sqrt{7}-\frac{1}{2}+6 \sqrt{11}\right)$ and $\left(\frac{1}{3} \sqrt{7}+\frac{3}{2} \sqrt{2}-\sqrt{11}\right)$

 

Solution:

(i) $2 \sqrt{3}-5 \sqrt{2}+\sqrt{3}+2 \sqrt{2}$

$=(2 \sqrt{3}+\sqrt{3})+(2 \sqrt{2}-5 \sqrt{2})$

$=3 \sqrt{3}-3 \sqrt{2}$

(ii) $2 \sqrt{2}+5 \sqrt{3}-7 \sqrt{5}+3 \sqrt{3}-\sqrt{2}+\sqrt{5}$

$=2 \sqrt{2}-\sqrt{2}+5 \sqrt{3}+3 \sqrt{3}+\sqrt{5}-7 \sqrt{5}$

$=\sqrt{2}+8 \sqrt{3}-6 \sqrt{5}$

(iii) $\frac{2}{3} \sqrt{7}-\frac{1}{2} \sqrt{2}+6 \sqrt{11}+\frac{1}{3} \sqrt{7}+\frac{3}{2} \sqrt{2}-\sqrt{11}$

$=\frac{2}{3} \sqrt{7}+\frac{1}{3} \sqrt{7}-\sqrt{11}+6 \sqrt{11}+\frac{3}{2} \sqrt{2}-\frac{1}{2} \sqrt{2}$

$=\sqrt{7}+5 \sqrt{11}+\sqrt{2}$

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