Respuesta :

the square root of 72x^2 = square root of ((6x)^2 )*2= 6x*square root of 2














Answer:

[tex]\text{The simplified expression is }6\sqrt x[/tex]          

Step-by-step explanation:

Given the radical expression

[tex]\sqrt{72x^2}[/tex]

we have to simplify the above expression.

[tex]Expression:\thinspace \sqrt{72x^2}[/tex]

Step 1: Factor 72 into its prime factors

[tex]72=2\times 2\times 2\times 3\times 3=2^3\times 3^2[/tex]

Step 2: Taking square root

[tex]\sqrt{72x^2}=\sqrt{2\times 2^2\times 3^2\times x^2}[/tex]

Step 3: Extract factors which are squares, i.e., factors that are raised to an even exponent.

[tex]\sqrt{72x^2}=2\times 3\times x\sqrt2=6\sqrt x[/tex]

which is required simplified form.