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Addition of Polynomials

If x × y=√x2+...

Question

If $x \times y = \sqrt{x^{2} + y^{2}}$ the value of $(1 \times 2 \sqrt{2}) (1 - 2 \sqrt{2})$ is.

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Solution

$x \times y = \sqrt{(x^{2} + y^{2})} (1 + 2 \sqrt{2}) (1 - 2 \sqrt{2}) = \sqrt{(1^{2} + (2 \sqrt{2})^{2})} = \sqrt{(1 + 8)} = \sqrt{9} = 3$

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