We have, 7√3√10+√3−2√5√6+√5−3√2√15+3√2.....(i)
Now, 7√3√10+√3×√10−√3√10−√3=7√30−21(√10)2−(√3)2 [by rationalisation]
[Using identity, (a−b)(a+b)=a2−b2]
7√30−2110−3=7(√30−3)7=√30−32√5√6+√5=2√5√6+√5×(√6−√5)√6−√5 [by rationalisation]
=2√30−10(√6)2−(√5)2 [Using identity ,(a−b)(a+b)=a2−b2]
=2√30−106−5=2√30−10
and 3√2√15+3√2=3√2√15+3√2×√15−3√2√15−3√2 [by rationlisation]
=3(√30−6)15−18=3(√30−6)−3=(−√30+6)=6−√30
From eq.(i). 7√3√10+√3−2√5√6+√5−3√2√15+3√2
=(√30−3)−(2√30−10)−(6−√30)=√30−3−2√30+10−6+√30=2√30−2√30+10−9=1