Question:
For which value of x must the expression √97x be further simplified?
A. 5 B. 10 C. 15 D. 20
Answer:
[tex]D.[/tex] [tex]x = 20[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{97x[/tex]
Required
For what value of x can it be simplified
From the list of options, only (D) is correct
D. 20
Substitute 20 for x in [tex]\sqrt{97x[/tex]
[tex]\sqrt{97 x} = \sqrt{97 * 20}[/tex]
Express 20 as 4 * 5
[tex]\sqrt{97 x} = \sqrt{97 * 4 * 5}[/tex]
Reorder
[tex]\sqrt{97 x} = \sqrt{4 *97 * 5}[/tex]
Split
[tex]\sqrt{97 x} = \sqrt{4} *\sqrt{97 * 5}[/tex]
[tex]\sqrt{97 x} = 2*\sqrt{97 * 5}[/tex]
[tex]\sqrt{97 x} = 2*\sqrt{485}[/tex]
[tex]\sqrt{97 x} = 2\sqrt{485}[/tex]
With other values of x, the given expression can not be simplified.
Hence:
[tex]x = 20[/tex]
