Question

simplify. 3√12 · 5√4

Explanation:

Step1: Multiply coefficients and radicals separately

$3\sqrt{12}\times5\sqrt{4}=(3\times5)\times(\sqrt{12}\times\sqrt{4})$

Step2: Calculate the product of coefficients

$3\times5 = 15$

Step3: Use the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ for radicals

$\sqrt{12}\times\sqrt{4}=\sqrt{12\times4}=\sqrt{48}$

Step4: Simplify $\sqrt{48}$

$\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}$

Step5: Multiply the result of coefficient - product and simplified radical

$15\times4\sqrt{3}=60\sqrt{3}$

Answer:

$60\sqrt{3}$