procedure by rational exponents

Problem:

Mr. Sanchez has two square lots for sale. One lot has length of side equal to 16m. The second lot has length of side equal to the diagonal of the first. What is the area of the second lot?

how is the problem justified in the procedure in simplifying rational exponents?

please help

thanks.

Re: procedure by rational exponents

The exact solution to the diagnol length of the first lot will have a rational exponent.

Do you know what it is?

Re: procedure by rational exponents

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Re: procedure by rational exponents

the diagonal of a square of side $\displaystyle x$ is $\displaystyle x\sqrt{2} = x \cdot 2^{1/2}$

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Re: procedure by rational exponents

Geometrically, if you construct a a new square having a diagonal of the first square as side, you should see that one-half of the first square forms one quadrant of the new square. The new square is (1/2)(4)= 2 times the area of the first.