Apply the formula (a+b)^2 = a^2 + 2ab + b^2
Hence,

(sqrt(2) + sqrt(5))^2
= (sqrt(2))^2 + 2(sqrt(2))(sqrt(5)) + ((sqrt(5))^2
= 2 + 2(sqrt(10)) + 5
= 7 + 2(sqrt(10))

Once you get to this, you need not calculate the exact value of sqrt(10).
Sqrt(9) is 3.. so sqrt(10) would be just over 3. So, we can assume sqrt(10) as 3, since the problem asks for approximate value.

So, the equation becomes = 7 + 2(3) = 13, C it is.

Hope this helps. Please share if you have any better ideas.

Since question is asking for an approximate answer something close to the rel answer is good enough.

2+5 + 2root(10)
Let's take the two cases you can check.
1. 2 + 5 + 2 root(9) = 13
2. 2 + 5 + 2 root(16) = 15

You know that root(10) is closer to root(9) than root(16)
hence 13 is the answer.

vinviper you should know square roots of 3 and 5, it will make you save time, use it as soon as you have this kind of problem and you will remember them fastly.
In this case you just add the two square roots you know and square it.