Question

A carpenter has three pieces of wood measuring √200, √72, and √18 inches. What is the total length when expressed in simplest radical form? (1 point)

Answer 1

To find the total length of the three pieces of wood when expressed in simplest radical form, we first simplify each radical:

1. **Simplifying \( \sqrt{200} \)**:
\[
\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \cdot \sqrt{2} = 10\sqrt{2}
\]

2. **Simplifying \( \sqrt{72} \)**:
\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}
\]

3. **Simplifying \( \sqrt{18} \)**:
\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\]

Next, we find the total length by adding these simplified radicals together:
\[
10\sqrt{2} + 6\sqrt{2} + 3\sqrt{2}
\]

Combining these:
\[
(10 + 6 + 3)\sqrt{2} = 19\sqrt{2}
\]

Thus, the total length of the wood is:
\[
\boxed{19\sqrt{2}}
\]