Question

Find the value of each expression
Square root of 8 + square root of 18 - square root of 32

Answer 1

To evaluate the expression \( \sqrt{8} + \sqrt{18} - \sqrt{32} \), we first simplify each square root.

1. **Simplify \( \sqrt{8} \)**:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]

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

3. **Simplify \( \sqrt{32} \)**:
\[
\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
\]

Now, we substitute the simplified values back into the original expression:
\[
\sqrt{8} + \sqrt{18} - \sqrt{32} = 2\sqrt{2} + 3\sqrt{2} - 4\sqrt{2}
\]

Next, we combine the terms:
\[
(2\sqrt{2} + 3\sqrt{2} - 4\sqrt{2}) = (2 + 3 - 4)\sqrt{2} = 1\sqrt{2} = \sqrt{2}
\]

Thus, the value of the expression \( \sqrt{8} + \sqrt{18} - \sqrt{32} \) is:
\[
\boxed{\sqrt{2}}
\]