Question

only simplify [3+2*2^(1/2)]^(1/2)​

Answer 1

Answer:

Step-by-step explanation:

[3+2×2^(1/2)]^(1/2)

3+4^(1/2)^(1/2)

3+2^2 (1/4)

3+2^(1/2) a^1/m=1/a^m

3+1/2^2

3+1/4 lcm of 3,4= 12

12+1/4

13/4

Answer 2

Step-by-step explanation:

√(3 + 2√(2))

=√(2 + 1 + 2√(2))

(because 3 can be written as 2 + 1)

=√(√(2)^2 + 1^2 +2*√(2)*1)

(because 2 can be written as √(2)^2 and 1 can be written as 1^2)

It shows the identity: (a+b)^2 = a^2 + b^2 + 2ab

So , it will become

[√(2+1)]^2

=(√2+1)^1/2*2

=[√2+1]^2/2

=[√2+1]^1

=√2+1

Therefore , the answer is √2 + 1

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