Sangeetha Pulapaka
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STEP 1: Recall what is a radical expression

STEP 2: Recall how to simplify a radical expression

STEP 3: Recall what are exponents

STEP 4: Recall the power rule of exponents

STEP 4: Recall what is product raised to a power rule

The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: (ab)x ax • bx

http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L2_T1_text_final.html

STEP 5: Use the rule

$\sqrt[x]{a}.\sqrt[x]{b} = \sqrt[x]{ab}$

To get,

\sqrt{12x^{3}}. \sqrt{3x} = \sqrt{12x^{3}.3x}

= \sqrt{12.3.x^{3}.x}

= \sqrt{36.x^{3+1}}

= \sqrt{36.x^{4}} (look for perfect squares in the radicand)

= \sqrt{6^{2}.(x^{2})^{2}} ( rewriting as the product of radicals)

= \sqrt{(6)^{2}}.\sqrt{(x^{2})^{2}}

= 6.x^{2}