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What is the simplified form of [tex][tex]$\sqrt{400 x^{100}}$[/tex][/tex]?

A. [tex][tex]$200 x^{10}$[/tex][/tex]
B. [tex][tex]$200 x^{50}$[/tex][/tex]
C. [tex][tex]$20 x^{10}$[/tex][/tex]
D. [tex][tex]$20 x^{50}$[/tex][/tex]

Sagot :

GinnyAnswer
To find the simplified form of [tex]\(\sqrt{400 x^{100}}\)[/tex], let's break down the expression step by step.

1. Square Root of the Constant:
[tex]\[ \sqrt{400} = 20 \][/tex]

2. Simplify the Exponent within the Radical:
[tex]\[ \sqrt{x^{100}} = x^{\frac{100}{2}} = x^{50} \][/tex]

3. Combine the Results:
[tex]\[ \sqrt{400 x^{100}} = 20 \cdot x^{50} \][/tex]

So, the simplified form of [tex]\(\sqrt{400 x^{100}}\)[/tex] is [tex]\(20 x^{50}\)[/tex].

Therefore, the correct option is:
[tex]\[ \boxed{20 x^{50}} \][/tex]
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