Question

Evaluate {√(5+2√6)} + {√(8-2√15)}

Answer 1

√(5+2√6)
=√(3+2+2√3.√2)
=√{(√3)²+2.√3.√2+(√2)²}
=√(√3+√2)²
=√3+√2 (neglecting the negative sign)
√(8-2√15)
=√(5+3-2.√5.√3)
=√{(√5)²-2.√5.√3+(√3)²}
=√(√5-√3)²
=√5-√3 (neglecting the negative sign)
∴, √(5+2√6)+√(8-2√15)
=√3+√2+√5-√3
=√2+√5 Ans.