Add-i 23-52 and3-22ii 22-53-75 and33-2-5iii 237-12-611 and137-322-11

(i) #160;23 52+3+22=23+3+22 52=33 32(ii) #160;22+53 75+33 2+5=22 2+53+33+5 75=2+83 65(iii) #160;237 122+611+137+322 11=237+137 11+611+322 122=7+511+2 ...

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Byju's Answer

Standard VI

Mathematics

Importance of Brackets

Add:i 23-52 a...

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

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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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Add: (i) 23-52and3+22 (ii) 22+53-75and33-2+5 (iii) 237-12+611and137+322-11

(i) 23-52+3+22=23+3+22-52=33-32(ii) 22+53-75+33-2+5=22-2+53+33+5-75=2+83-65(iii) 237-122+611+137+322-11=237+137-11+611+322-122=7+511+2

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