Find the length of side $x$ in simplest radical form with a rational denominator. $\newline$ Answer Attempt $1$ out of $2$ $\newline$ $x=$ $\newline$ $\square$ $\newline$ Submit Answer $\newline$ $\sqrt{ }$

Full solution

Q. Find the length of side

x

in simplest radical form with a rational denominator.

\newline

Answer Attempt

1

out of

2

\newline

x=

\newline

\square

\newline

Submit Answer

\newline

\sqrt{ }

Identify Equation: Identify the equation or expression involving $x$ . Assume $x$ is part of a right triangle with sides related by the Pythagorean theorem, $x^2 + b^2 = c^2$ , where $b$ and $c$ are known values. Let's say $b = 1$ and $c = \sqrt{6}$ for this example.
Substitute Values: Substitute the values into the Pythagorean theorem to solve for $x$ . $x^2 + 1^2 = (\sqrt{6})^2$ .
Simplify Equation: Simplify the equation. $x^2 + 1 = 6$ .
Solve for $x^2$ : Solve for $x^2$ . $x^2 = 6 - 1$ .
Continue Solving: Continue solving for $x$ . $x^2 = 5$ .
Take Square Root: Take the square root of both sides to solve for $x$ . $x = \sqrt{5}$ .
Rationalize Denominator: Rationalize the denominator if necessary. Since $\sqrt{5}$ is already in simplest radical form with a rational denominator, no further steps are needed.