Respuesta :
Answer:
The correct option is B.
Step-by-step explanation:
The given expression is
[tex]\sqrt{144x^{36}}[/tex]
Use the property of radicals.
[tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\sqrt{144x^{36}}=\sqrt{144}\times \sqrt{x^{36}}[/tex]
Use the property of exponent.
[tex]a^{mn}=(a^m)^n[/tex]
[tex]\sqrt{144x^{36}}=12\times \sqrt{(x^{18})^2}[/tex]
[tex]\sqrt{144x^{36}}=12\times x^{18}[/tex]
[tex]\sqrt{144x^{36}}=12x^{18}[/tex]
Therefore option B is correct.
Answer:
Option (b) is correct.
Expression becomes [tex]=12x^{18}[/tex]
Step-by-step explanation:
Given : square root of [tex]144x^{36}[/tex]
We have to write the given expression in simplified form.
Consider the given expression square root of [tex]144x^{36}[/tex]
Mathematically written as [tex]\sqrt{144x^{36}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},[/tex]
We have,
[tex]=\sqrt{144}\sqrt{x^{36}}[/tex]
We know [tex]\sqrt{144}=12[/tex]
[tex]=12\sqrt{x^{36}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]\sqrt{x^{36}}=x^{\frac{36}{2}}=x^{18}[/tex]
Thus, Expression becomes [tex]=12x^{18}[/tex]
