Question

1. Find the square root of 14 +6 under root 5​

Answer 1

Answer:

3+√5

Step-by-step explanation:

hope it helps..

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Answer 2

Answer:

we know that:-

(√a + √b)² = a + b + 2√ab

now,

(14 + 6√5) is a perfect square

let (14 + 6√5) = (a + b) + 2√ab

on comparing both side s

we get,

a + b = 14   -(1)

AND,

6√5 = 2√ab

=> 3√5 = √ab

=> 45 = ab   -(2)

we know that:-

(a - b)² = (a + b)² - 4ab

=> (a - b)² = (14)² - 4×45

=> (a - b)² = 196 - 180

=> (a - b)² = 16

=> (a - b)² = 4²

=> a - b = 4  -(3)

now,

from -(1) AND-(3)

we get,

a + b = 14

a - b = 4

2a = 18

=> a = 9 put in--(2)

we get,

9×b = 45

=> b = 45/9

=> b = 5 and, a = 9

now,

the square root of √(14 + 6√5) = (√9 + √5)

=> (3 + √5)

verification,

(3 + √5)² = 3² + (√5)² + 2×3×√5

=> 9 + 5 + 6√5

=> 14 + 6√5

Hope this helps