Question

simplify :
2√6/√2+√3 + 6√2/√6+√3

Answer 1

root6/root2=root3
6×root 2÷root6=2 root3
2root3+root3+2root3+root3=6root3

Answer 2

We know that (√a+√b)2= a+b+2√ab
Now √(5 + 2√6). If it is a perfect sq,
there will be 2 no.s - such that a + b = 5.2√ab = 2√6
⇒ ab = 6
(a=3, b=2)so that, 5 + 2√6
= 3+2+2√(3×2)=(√3+√2)2∴ √( 5 + 2√6)
= √3+√2.
similarly, Consider √(8 - 2√15)a + b = 8 ⇒ ab
= 15 (a = 5,b = 3)√(8 - 2√15) = (√5 - √3)
Now √( 5 + 2√6) + √(8 - 2√15)
= √3 + √2 + √5 - √3 = √2 + √5.