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Question

# Find the value of 26−15√3[5√2−√38+5√3]2+√10+√18√8+√(3−√5).

A
13
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B
23
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C
35
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D
73
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Solution

## The correct option is D 73√8+√3−√5=(√8+√3−√5)√2√2=1√2(4+√6−2√5)6−2√5=1√2(4+√(√5−1)2) =1√2(4+√5−1) =(√5−1)2=1√2(3+√5)√10+√18√8+√3−√5=√10+√181√2(3+√5)= √20+√363+√5=2√5+63+√5=25√5−√38+5√3=1√2[√2(5√2−√38+5√3)]=1√2[10−√76+2√75]=1√2[10−√(√75+√1)2]=1√2[10−(√75+1)]=1√2[9−√75]26−15√3[5√2−√38+5√3]2=26−15√3[1√2(9−√75)]2=2(26−15√3)75−2(9)\$√7552−30√3156−90√3=52−30√33(52−30√3)=13∴√10+s√18√8+√3−√5+26−15√3[5√2−√38+5√3]2=2+13=73

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