jaemehoward21
contestada

PLEASE HELP!!! URGENT!!!

Simplify 512xm3‾‾‾‾‾‾√ .

Assume x and m are nonnegative.




10m33x‾‾√

60m3x√

60xm3‾‾‾‾√

10m3xm‾‾‾‾√

Respuesta :

tramserran

After you reposted, I see the actual question is: 5[tex]\sqrt{12xm^{3} }[/tex].  I am going to leave the information below since it will be helpful for you going forward in the class.

5[tex]\sqrt{12xm^{3} }[/tex]

= 5[tex]\sqrt{2*2*3*x*m*m*m}[/tex]

= 5[tex]\sqrt{(2*2)*3*x*m*(m*m)}[/tex]

= 5*2*m[tex]\sqrt{3*x*m}[/tex]

= 10m[tex]\sqrt{3xm}[/tex]

**********************************

I am going to assume that the problem is actually [tex]\sqrt{512xm^{3} }[/tex]

= [tex]\sqrt{2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * x * m * m * m}[/tex]

Look for groups of 2 (since it is square root)

=  [tex]\sqrt{(2 * 2) * (2 * 2) * (2 * 2) * (2 * 2) * 2 * x * m * (m * m)}[/tex]

Bring ONE of each pair outside the square root and leave the rest inside

= 2 * 2 * 2 * 2 * m  [tex]\sqrt{ 2 * x * m}[/tex]

= 16m[tex]\sqrt{ 2xm}[/tex]


If the question is actually "cubed root" and not square root, then do the same as above except look for groups of 3.

MrRoyal

The expression is given in index form

The result of the simplifying [tex]\sqrt{512xm^3}[/tex] is: [tex]16m\sqrt{2xm}[/tex]

We have:

[tex]\sqrt{512xm^3}[/tex]

Express 512 as an exponent

[tex]\sqrt{512xm^3} = \sqrt{2^9xm^3}[/tex]

Expand

[tex]\sqrt{512xm^3} = \sqrt{2^8 \times 2 \times x \times m^2 \times m}[/tex]

Split

[tex]\sqrt{512xm^3} = \sqrt{2^8} \times \sqrt{2} \times \sqrt{x} \times \sqrt{m^2} \times \sqrt{m}[/tex]

Evaluate all square roots

[tex]\sqrt{512xm^3} = 2^4 \times \sqrt{2} \times \sqrt{x} \times m \times \sqrt{m}[/tex]

[tex]\sqrt{512xm^3} = 16 \times \sqrt{2} \times \sqrt{x} \times m \times \sqrt{m}[/tex]

Rewrite as:

[tex]\sqrt{512xm^3} = 16 \times m\times \sqrt{2 \times x \times m}[/tex]

[tex]\sqrt{512xm^3} = 16m\times \sqrt{2xm}[/tex]

[tex]\sqrt{512xm^3} = 16m\sqrt{2xm}[/tex]

Hence, the result of the simplification is: [tex]16m\sqrt{2xm}[/tex]

Read more about simplification of expressions at:

https://brainly.com/question/2795666

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