Question

the value
$\sqrt{17 + 12 \sqrt{2} } \: is \: closest \: to$
​

Answer 1

Answer:

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Answer 2

In these type of questions ,the approach should be to remove the complicated radicals.Mostly the term inside the root will be a whole square or whole cube.

So

17+12(2)^1/2=(3+2(2)^1/2)^2

and

17–12(2)^1/2=(3–2(2)^1/2)^2

also 3+2(2)^1/2=(1+2^1/2)^2

and

3–2(2)^1/2=(1–2^1/2)^2

so

17+12(2)^1/4=1+2^1/2 ……………………………………………(1)

and

17–12(2)^1/4=2^1/2…………………………………………………(2)

so

subtracting equation (1) and (2) the answer comes 2.

Hence proved.