sqare root expression

[lukezo]

Hi,

can you help me out with this problem:

https://ibb.co/gwkqW9F

The task is to solve it without calculator. Result is square root (2)
...................... added the image

Thanks.

 

[Deleted member 4993]

Hi,

can you help me out with this problem:

https://ibb.co/gwkqW9F

The task is to solve it without calculator. Result is square root (2)

Thanks.

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Please share your work/thoughts about this problem.

 

[Alekos]

Start by squaring 4sqrt(2+sqrt3) - 4 sqrt(2-sqrt3) then take the square root and then subtract this this to the square of (2-sqrt10)sqrt(7+2sqrt10)

 

[Dr.Peterson]

Hi,

can you help me out with this problem:

The task is to solve it without calculator. Result is square root (2)

Thanks.

Start by squaring 4sqrt(2+sqrt3) - 4 sqrt(2-sqrt3) then take the square root and then subtract this this to the square of (2-sqrt10)sqrt(7+2sqrt10)

Not quite stated correctly, but this is a good hint.

Separately simplify [imath]4\sqrt{2+\sqrt{3}} - 4\sqrt{2-\sqrt{3}}[/imath] and [imath](2-\sqrt{10})\sqrt{7+2\sqrt{10}}[/imath] by squaring each expression, and taking the square root of the results.

 

[P.K.Tandon]

Yes. Dr. Peterson I also did the same and got the result = 7* sqrt(10)

 

[Dr.Peterson]

Yes. Dr. Peterson I also did the same and got the result = 7* sqrt(10)

I get the expected [imath]\sqrt{2}[/imath] this way; and you can also verify it using a calculator.

 

[lukezo]

Dr.Peterson: +1

Thank you all for your contribution!