Answer: [tex]6\sqrt{2}-30\sqrt{3}[/tex]
Step-by-step explanation:
Remember that:
[tex](\sqrt{a})(\sqrt{b})=\sqrt{ab}[/tex]
[tex]\sqrt[n]{a^n}=a[/tex]
Given the following expression:
[tex](2-5\sqrt{6})(3\sqrt{2})[/tex]
The steps to simplify this expression, are:
1. Apply the Distributive property:
[tex]=(2)(3\sqrt{2})-(5\sqrt{6})(3\sqrt{2})=6\sqrt{2}-15\sqrt{12}[/tex]
2.Since:
[tex]12=2*2*3=2^2*3[/tex]
You can rewrite the radicand 12 in this form:
[tex]=6\sqrt{2}-15\sqrt{2^2*3}[/tex]
3. Simplifying, you get:
[tex]=6\sqrt{2}-(15)(2)\sqrt{3}=6\sqrt{2}-30\sqrt{3}[/tex]
4. Notice that the indices of the Radicals are the same, but the radicands don't, then, you can subtract the Radicals.
