Respuesta :
Answer:
(a) [tex]\sqrt{x^3} = x\sqrt{x}[/tex]
(b)[tex]\sqrt{a^5} = a^2\sqrt{a}[/tex]
Step-by-step explanation:
Here, the given expression is :
[tex](a) \sqrt{x^3}[/tex]
Now, cube of any number [tex]a = (a)^3 = a \times a \times a[/tex]
So, [tex] (x)^3 = x \times x \times x = (x) ^2 \times x[/tex]
[tex]\implies \sqrt{x^3} = \sqrt{x^2 \times x} = \sqrt{x^2}\sqrt{x} = x\sqrt{x}[/tex]
(because [tex]\sqrt{a^2} = a[/tex])
Hence, [tex]\sqrt{x^3} = x\sqrt{x}[/tex]
Here, the given expression is :
[tex](b) \sqrt{a^5}[/tex]
Now, five power of any number [tex]m = (m)^5 = m \times m \times m \times m \times m [/tex]
So, [tex] (x)^5 = x \times x \times x \times x \times x = (x) ^4 \times x[/tex]
[tex]\implies \sqrt{a^5} = \sqrt{a^4 \times x} = \sqrt{a^4}\sqrt{a} = a^2\sqrt{x}[/tex]
(because [tex]\sqrt{a^4} = a^2[/tex])
Hence, [tex]\sqrt{a^5} = a^2\sqrt{a}[/tex]
