Answer:
Prime Factorization of 576
[tex]576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3[/tex]
Prime Factorization of 64
[tex]64=2\times 2\times 2\times 2\times 2\times 2[/tex]
The Expression in simplest form is
[tex]\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}[/tex]
Step-by-step explanation:
Simplify:
[tex]\sqrt{\dfrac{576}{64} }[/tex]
Now,
Prime Factorization of 576
[tex]576=2\times 288\\576=2\times 2\times 144\\576=2\times 2\times 2\times 72\\576=2\times 2\times 2\times 2\times 36\\576=2\times 2\times 2\times 2\times 2\times 18\\576=2\times 2\times 2\times 2\times 2\times 2\times 9\\576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3[/tex]
Prime Factorization of 64
[tex]64=2\times 32\\64=2\times 2\times 16\\64=2\times 2\times 2\times 8\\64=2\times 2\times 2\times 2\times 4\\64=2\times 2\times 2\times 2\times 2\times 2[/tex]
Now,
[tex]\sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}{2\times 2\times 2\times 2\times 2\times 2} }\\ \sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{3\times 3}{1}}\\\therefore \sqrt{\dfrac{576}{64} }=3[/tex]
The Expression in simplest form is
[tex]\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}[/tex]
