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Section 6.2 Radical Expressions Summary
Adding/subtracting like radicals
\(\rightarrow\) add the front numbers
Multiply radicals
\(\rightarrow\) multiply everything together
Subsection 6.2.1 Examples
Example 6.2.1 .
A rectangle has dimensions
\(6+\sqrt{3}\) and
\(6-\sqrt{3}\text{.}\) Find its area.
Example 6.2.2 .
Show that the reciprocal of
\(\sqrt{26}-5\) is 10 greater than
\(\sqrt{26}-5\text{.}\)
Hint .
Take the reciprocal and rationalize the denominator.
Example 6.2.3 .
Determine the value of
\(x\) if the diagonal of Rectangle 2 is three times the length of the diagonal of Rectangle 1.
Figure 6.2.4. Two rectangles with radical dimensions
Hint .
First find an expression for each diagonal, using the Pythagorean theorem, then set up an equation.
Answer .
Example 6.2.5 .
The point
\(P\) lies on the
\(y\) -axis. The coordinates of
\(R\) and
\(S\) are
\((-21, 0)\) and
\((15, 0)\) respectively. The sum of
\(PR\) and
\(PS\) is 54 units. Determine the coordinates of
\(P\text{.}\)
Figure 6.2.6. Point P on the y-axis with distances to R and S
Hint .
Using the distance formula,
\(\sqrt{441+y^2}+\sqrt{225+y^2}=54\text{,}\) then solve for
\(y\text{.}\)
Answer .
\(P = (0, 20)\) or
\(P = (0, -20)\)
Example 6.2.7 .
The area of the given triangle is 30 m
\(^2\text{.}\) Determine the value of
\(x\text{.}\)
Figure 6.2.8. Right triangle with radical side lengths
Hint .
Use the triangle area formula
\(A = \frac{1}{2}bh\text{,}\) then solve the resulting quadratic equation.
Answer .
