Question

find the square root of 5+2√6​

Answer 1

Answer:√3+√2

Step-by-step explanation:

√5+2√6

=√3+2+2×√3×√2

(√a+b+2√ab=√a+√b)

=√3+√2.

Answer 2

Given:

expression: 5+2√6​

To Find:

The square root of 5+2√6​.

Solution:

We have,

5+2√6,  

{ a = m × n

∴ √a = √m × √n }

can be written as

⇒ 5 + 2(√.3.√2​)

{ ∵  5 = (√3)² + (√2)² }

⇒ (√3)² + (√2)² + (2.√3.√2)

{ a² + b² + 2ab = ( a + b )²

⇒ ∴ (√3+√2)².

Now,

the square root of 5+2√6

​ is ​$(\sqrt{3}+\sqrt{2} )^{2.1/2}$ =  (√3​+√2​)

Hence, the square root of 5+2√6​ is   (√3​+√2​).