Respuesta :
[tex]\bf 2\sqrt{54}+5\sqrt{24}\qquad \begin{cases} 54=2\cdot 3\cdot 3\cdot 3\\ \qquad 2\cdot 3\cdot 3^2\\ \qquad 6\cdot 3^2\\ 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 6 \end{cases}\implies 2\sqrt{6\cdot 3^2}+5\sqrt{2^2\cdot 6} \\\\\\ 6\sqrt{6}+10\sqrt{6}\implies \stackrel{\textit{adding like-terms}}{16\sqrt{6}}[/tex]
The simplest radical form of the equation [tex]2\sqrt{54} + 5\sqrt{24}[/tex] is [tex]16 \sqrt{6}[/tex].
We have to determine, the simplest radical form [tex]2\sqrt{54} + 5\sqrt{24}[/tex].
To convert the given equation into radical form following all the steps given below.
Equation; [tex]2\sqrt{54} + 5\sqrt{24}[/tex].
- Step1; Converting 254 or 524 into small factors.
[tex]= 2\sqrt{54} + 5\sqrt{24}\\\\=2 \sqrt{2 \times 3 \times 3 \times 3} + 5\sqrt{2 \times 2 \times 2\times 3}[/tex]
- Step2; There are squares of 2 and 3 so the making square and remove from the square root.
[tex]=2 \sqrt{2 \times 3 \times 3 \times 3} + 5\sqrt{2 \times 2 \times 2\times 3}\\\\= 2 \sqrt{2 \times 3 \times 3^2} + \sqrt{2^2\times 2 \times 3} \\\\[/tex]
- Step3; Now multiply the terms and solve the equation.
[tex]= 2\times 3\ \sqrt{2 \times 3 } + 5 \times 2 \sqrt{2 \times 3}\\\\= 6 \sqrt{6} \ + 10 \ \sqrt{6}\\\\= 16\sqrt{6}[/tex]
Hence, The required simplest radical form of the equation [tex]2\sqrt{54} + 5\sqrt{24}[/tex] is [tex]16 \sqrt{6}[/tex]
To know more about the Radical form click the link given below.
https://brainly.com/question/12186700
