Respuesta :
Question:
Which is equivalent to [tex]\sqrt{180x^{11}}[/tex] after it has been simplified completely?
Answer:
[tex]\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{180x^{11}}[/tex]
Required
Simplify
We start by splitting the square root
[tex]\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}[/tex]
Replace 180 with 36 * 5
[tex]\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}[/tex]
Further split the square roots
[tex]\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}[/tex]
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}[/tex]
Replace power of x; 11 with 10 + 1
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}[/tex]
From laws of indices; [tex]a^{m+n} = a^m * a^n[/tex]
So, we have
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}[/tex]
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}[/tex]
Further split the square roots
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}[/tex]
From laws of indices; [tex]\sqrt{a} = a^{\frac{1}{2}}[/tex]
So, we have
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}[/tex]
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}[/tex]
[tex]\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}[/tex]
Rearrange Expression
[tex]\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}[/tex]
[tex]\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}[/tex]
From laws of indices; [tex]\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}[/tex]
So, we have
[tex]\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}[/tex]
[tex]\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}[/tex]
[tex]\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}[/tex]
The expression can no longer be simplified
Hence, [tex]\sqrt{180x^{11}}[/tex] is equivalent to [tex]6x^{5}\sqrt{5x}[/tex]
Answer:
D on edg
Step-by-step explanation:
6x^5 V5x is correct
