College

Which choice is equivalent to the expression below?

[tex]\sqrt{32} - \sqrt{2}[/tex]

A. [tex]16 \sqrt{2}[/tex]
B. [tex]\sqrt{30}[/tex]
C. [tex]3 \sqrt{2}[/tex]
D. 4

Answer :

To simplify the expression
[tex]$$
\sqrt{32} - \sqrt{2},
$$[/tex]
we first simplify the square root term [tex]$\sqrt{32}$[/tex].

Step 1: Express 32 as a product of a perfect square and another number. Notice that
[tex]$$
32 = 16 \times 2.
$$[/tex]

Step 2: Rewrite [tex]$\sqrt{32}$[/tex] using the product under the square root:
[tex]$$
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2}.
$$[/tex]

Step 3: Evaluate the square root of 16:
[tex]$$
\sqrt{16} = 4,
$$[/tex]
so we have
[tex]$$
\sqrt{32} = 4\sqrt{2}.
$$[/tex]

Step 4: Substitute [tex]$\sqrt{32} = 4\sqrt{2}$[/tex] back into the original expression:
[tex]$$
\sqrt{32} - \sqrt{2} = 4\sqrt{2} - \sqrt{2}.
$$[/tex]

Step 5: Combine like terms by subtracting the coefficients:
[tex]$$
4\sqrt{2} - \sqrt{2} = (4 - 1)\sqrt{2} = 3\sqrt{2}.
$$[/tex]

Thus, the expression simplifies to
[tex]$$
3\sqrt{2}.
$$[/tex]

The equivalent choice is [tex]$\boxed{3\sqrt{2}}$[/tex].