Question

evaluate
$\sqrt{5 + 2 \sqrt{6} }$

Answer 1

heya...!!!!!


we know that:-

(√a + √b)² = a + b+ 2√ab

[√(5 + 2√6)] if it is a perfect square

now, on comparing both side

we get,

a + b = 5---------(1)

2√ab = 2√6

=> √ab = √6

=> ab = 6-----(1)

as we know,

(a - b)² = (a + b)² - 4ab

=> (a - b)² = (5)² - 4×6

=> (a - b)² = 25 - 24

=> a - b = 1------(3)

from---(1) and ---(3)

a + b = 5
a - b = 1
—————
2a = 6

=> a = 3 put in--(2)

we get,


3×b = 6

=> b = 6/3

=> b = 2

now,

[(5 + 2√6)] = 3 + 2 + 2√2×3

=> (√3 + √2)²

=> [√(5 + 2√6)] = (√3 + √2)