Question

Find the square root of 14+6√5​

Answer 1

Answer:

3 + √5

Step-by-step explanation:

Find the square root of 14+6√5​

Change to √ ( 14 + 6√5 ) = √x + √y

1️⃣ Square.

14 + 6√5 = x + y + 2√xy

14 + 2√45 = ( x + y) + 2√xy

2️⃣ Compare.

(x + y) = 14

xy = 45

3️⃣ Solve.

(x - y)² = (x+y)² - 4xy

( x - y)² = 14² - 180

( x - y)² = 196 - 180

( x - y)² = 16

( x - y) = 4

x + y = 14

x - y = 4

2x = 18

x = 9 .

y = 5 .

14 + 6√5 = √9 + √5 = 3 + √5 .

Answer: 3 + √5 .

Done ✔