Question

Evaluate under root 5 + 2 under root 6 + under root 8 minus 2 under root 15

Answer 1

Question given:  pls evaluate {whole root(5+2 root 6)} + {Whole root(8-2 root 15)}

Sol: 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.