1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Simplify: (i) √5+√3√5−√3+√5−√3√5+√3 (ii) 12+√3+2√5−√3+12−√5 (iii) 2√5+√3+1√3+√2−3√5+√2

Open in App
Solution

## (i) √5+√3√5−√3+√5−√3√5+√3=(√5+√3)2+(√5−√3)2(√5−√3)(√5+√3)=2[(√5)2+(√3)2](√5)2−(√3)2 {∵(a+b)2+(a−b)2=2(a2+b2)}=2(5+3)5−3=2×82=8 (ii) 12+√3=1(2−√3)(2+√3)(2−√3)=1(2−√3)(2)2−(√3)2=2−√34−3=2−√31=2−√32√5−√3=2(√5+√3)(√5−√3)(√5+√3)=2(√5+√3)(√5)2−(√3)2=2(√5+√3)5−3=2(√5+√3)2=√5+√312−√5=1(2+√5)(2−√5)(2+√5)=2+√5(2)2−(√5)2=2+√54−5=2+√5−1=(−2−√5)Now, 12+√3+2√5−√3+12−√5=(2−√3)+(√5+√3)+(−2−√5)=2−√3+√5+√3−2−√5=0 (iii) 2√5+√3=2(√5−√3)(√5+√3)(√5−√3)=2(√5−√3)(√5)2−(√3)2=2(√5−√3)5−3=2(√5−√3)2=√5−√31√3+√2=1×(√3−√2)(√3+√2)(√3−√2)=√3−√2(√3)2−(√2)2=√3−√23−2=√3−√21=√3−√23√5+√2=3(√5−√2)(√5+√2)(√5−√2)=3(√5−√2)(√5)2−(√2)2=3(√5−√2)5−2=3(√5−√2)3=√5−√2Now, 2√2+√3+1√3+√2−3√5+√2=√5−√3+√3−√2−(√5−√2)=√5−√3+√3−√2−√5+√2=0

Suggest Corrections
11
Join BYJU'S Learning Program
Related Videos
Identities for Irrational Numbers
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program