Question

solve this pleaseeeeee i will follow and award 20 points Express with a rational denominator ​

Answer 1

1/(√10+√14+√15+√21) 1/(√(2×5)+√(2×7)+√(3×5)+√(3×7)) 1/(√2×√5+√2×√7+√3×√5+√3×√7) =1/{(√2)(√5+√7)+√3(√5+√7)} =1/{(√5+√7)(√2+√3)} Rationalize the denominator by Multiplying numerator and denominator by (√5−√7)(√2−√3), we get 1/{(√5+√7)(√2+√3)}={1×(√5−√7)(√2−√3)}/{(√5+√7)(√2+√3)(√5−√7)(√2−√3)} ={1×(√5−√7)(√2−√3)}/{(√5+√7)(√5−√7)(√2+√3)(√2−√3)} ={1×(√5−√7)(√2−√3)}/[{(√5)²−(√7)²}{(√2)²−(√3)²}] ={(√5−√7)√2−(√5−√7)√3)}/{(5−7)}(2−3)}=(√5×√2−√7×√2−√5×√3+√7×√3)/{(−2)}(−1)} =(√10−√14−√15+√21)/(2)} =½(√21−√15−√14+√10)