Mathematics: Simplify this expression ( 2-5 square root 6) x 3 square root of 2

Simplify this expression ( 2-5 square root 6) - id25634157580, kovacscsilla55owjvhn

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12.01.2022

$6\sqrt{2}-30\sqrt{3}$

Step-by-step explanation:

Remember that:

$(\sqrt{a})(\sqrt{b})=\sqrt{ab}$

$\sqrt[n]{a^n}=a$

Given the following expression:

$(2-5\sqrt{6})(3\sqrt{2})$

The steps to simplify this expression, are:

1. Apply the Distributive property:

$=(2)(3\sqrt{2})-(5\sqrt{6})(3\sqrt{2})=6\sqrt{2}-15\sqrt{12}$

2.Since:

12=2*2*3=2^2*3

You can rewrite the radicand 12 in this form:

$=6\sqrt{2}-15\sqrt{2^2*3}$

3. Simplifying, you get:

$=6\sqrt{2}-(15)(2)\sqrt{3}=6\sqrt{2}-30\sqrt{3}$

4. Notice that the indices of the Radicals are the same, but the radicands don't, then, you can subtract the Radicals.

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