Question

Prove square root of14+6root5 is equal to 3root5

Answer 1

⊕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

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

Answer 2

Answer:

Step-by-step explanation:

14 + 6 root 5 = 14 + 6(2.236) = 14 + 13.416 = 27.416

square root of 27.416 = 5.236

3 root 5 = 3(2.236) = 6.708

square root of 14 + 6 root 5 is not equal to 3 root 5