Question

What is the square root of 9+2√14 *

Answer 1

Answer:

We know that

(√a+√b)² = a + b + 2√ab

Now √(9 + 2√14). If it is a perfect sq,

so, there will be 2 numbers

such that:-

a + b = 9---------( 1 )

2√ab = 2√14 ⇒ ab = 14

using formula:- (a - b)² = (a + b)² - 4ab

(a - b)² = (9)² - 4(14)

(a - b)² = 81 - 56

(a - b)² = 25  

(a - b) = 5--------( 2 )  

from------( 1 ) & --------( 2 )  

a + b = 9

a - b = 5

–—–—–

2a = 14  

a = 7 [ put in ---( 1 ) ]

a + b = 9  

b = 9 - 7

b = 2  

thus, a = 7 , b = 2

therefore, √(9 + 2√14) = √(√7 + √2)²  

= (√7 + √2)

Step-by-step explanation:

Answer 2

Step-by-step explanation:

here is ur answer

hope it helps