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Find the side of x in simplest radical form with a rational denominator

Find the side of x in simplest radical form with a rational denominator-example-1

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Since we have a 45 degree right triangle , both legs of the triangle (other than x ) are equal by its definition.

By Pythagorean Theorem, we can express x as


\begin{gathered} x^2=6^2+6^2 \\ x=\sqrt[\square]{36+36} \\ x=\sqrt[\square]{72} \\ x=\sqrt[\square]{36\cdot2} \\ x=6\sqrt[\square]{2} \end{gathered}

Answer:


x=6\sqrt[\square]{2}

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