Question

find the length of side x in simplest radical form with a rational denominator.
answer attempt 1 out of 2
x =
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Explanation:

Step1: Identify triangle type

The triangle is isosceles right - angled (two legs equal, right angle). Let the legs be \(a = 8\), \(b = 8\), hypotenuse \(x\).

Step2: Apply Pythagorean theorem

Pythagorean theorem: \(x^{2}=a^{2}+b^{2}\). Substitute \(a = 8\), \(b = 8\):
\(x^{2}=8^{2}+8^{2}=64 + 64=128\).

Step3: Simplify radical

\(x=\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\) (since \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\), \(a = 64\), \(b = 2\), \(\sqrt{64}=8\)).

Answer:

\(8\sqrt{2}\)