√√(√7+√2)=?

Question

Please simplify this equation. I know the right answer is √3, but I don't know how to process it.

Please help me to figure out this question. Thank you very much.

Thanks to those people who answer my question previously. To avoid any mistake with my current question, I would like to put the original equation instead of the current one. So please ignore the equation I put before. Now I change my original equation to the new one. Please help me to figure out.

√√[(√7)one-third power＋(√2)one-third power]×√√[(√49)one-third power－(√14)one-third power＋(√4)one-third power]=?

Thank you very much!

Answer 1

Here is the answer, but if you want it to be √3, then you should remove the sq. root signs from inside the brackets.

√√[(7)^(1/3)＋(2)^(1/3)] ×√√[(49)^(1/3)－(14)^(1/3)＋
(4)^(1/3)]=

√√ { [(7)^(1/3)＋(2)^(1/3)] ×[(49)^(1/3)－(14)^(1/3)＋
(4)^(1/3)] } =

√√ { [(7)^(1/3)＋(2)^(1/3)] ×[(7)^(2/3) -[(7)^(1/3)][(2)^(1/3)] + (2)^(2/3)] }


expand what's inside the brackets:

=√√ { (7)^(3/3) - [(7)^(2/3)][(2)^(1/3)] + [(7)^(1/3)][(2)^(2/3)] +
[(2)^(1/3)][(7)^(2/3)] - [(2)^(2/3)][(7)^(1/3)] + (2)^(3/3) }

= √√ { (7)^(3/3) + (2)^(3/3) } = √√ { 7+2 } = √√ (9) = √3

Answer 2

assume
√√(√7+√2)=x
rising x to the power 4 we have,
√7+√2=x to the power 4
soving this we get value of x and that is the answer

Answer 3

√√(√7+√2)=x
(7+2)=x to the power of two
9 = 3x3

Answer 4

It doesnt even make sense.
Assume that the correct answer is the square root of 3 then that would be 1.732.

the square root of 7 is 2.645713
and the square root of 2 is 1.412
add those both together and you get = 4.057713
the square root of the square root of 4.057713 is 1.419

so the answer would be 1.419 which is the square root of 2.014

So basically I have no idea if the answer you say is right but that is how I would work it out.

Answer 5

The right answer is not V3.
The approximate value is
1.4194842202124163157689184540705


The radicals cannot be simplified. Sqrt(2) and Sqrt(7) are rationally independent algebraic numbers.

Answer 6

break it down into parts:

step 1: solve this portion first: square root of 7, square root of 2.
step 2: add the two together
step 3: find the square root of that answer
step 4: find the square root of the square root of the answer.

i.e. sqrt{sqrt [sqrt(7) + sqrt(2)]}

it follows the same rule as BEDMAS

Answer 7

√√(√7+√2)=x
√(√7+√2)=x^2
√7+√2=x^4
(√7+√2)(√7+√2)=x^8
7+√14+√14+2=x^8
9+2√14=x^8
√√√(9+2√14)=x

But that still doesn't seem very simple to me... are you sure you got the question right?

Answer 8

sqrt(sqrt(sqrt(7) +sqrt(2)) ? sqrt(3)
sqrt(sqrt(7)+sqrt(2)) ? 3
sqrt(7) + sqrt(2) ? 9
7+2+ 2sqrt(14) ? 81
sqrt(14) ? 36
14 <> 36*36
So the answer cannot be sqrt(3).

Answer 9

No,the answer is not sqrt(3). It really can't be simplified further.