High School

Which choice is equivalent to the expression below?

[tex]\sqrt{50} - \sqrt{2}[/tex]

A. [tex]24 \sqrt{2}[/tex]
B. 5
C. [tex]\sqrt{48}[/tex]
D. [tex]4 \sqrt{2}[/tex]

Answer :

First, note that the square root of 50 can be simplified as follows:

[tex]$$
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25}\sqrt{2} = 5\sqrt{2}.
$$[/tex]

Replacing [tex]$\sqrt{50}$[/tex] in the original expression gives:

[tex]$$
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}.
$$[/tex]

Now, combine like terms by subtracting the coefficients of [tex]$\sqrt{2}$[/tex]:

[tex]$$
5\sqrt{2} - \sqrt{2} = (5-1)\sqrt{2} = 4\sqrt{2}.
$$[/tex]

Thus, the expression [tex]$\sqrt{50} - \sqrt{2}$[/tex] is equivalent to [tex]$4\sqrt{2}$[/tex], which corresponds to option D.