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.

Answer 2

Answer:

√(5+2√6)

=√(3+2+2×√3×√2)

=√(√3+√2)^2

=√3+√2

√(8-2√15)

=√(5+3-2×√5×√3)

=√(√5-√3)^2

=√5-√3

So

√(5+2√6)+√(8-2√15)

= √3+√2+√5-√3

= √2+√5 or √5+√2

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