Sangeetha Pulapaka
0

STEP 1: Recall what is a radical expression

https://study.com/academy/lesson/radical-expression-definition-examples-quiz.html

STEP 2: Recall how to simplify a radical expression

https://www.mathplanet.com/education/algebra-1/radical-expressions/simplify-radical-expressions

STEP 3: Recall what are exponents

www.qalaxia.com/viewDiscussion?messageId=5cdad642f32dc9584bdccefe

STEP 4: Recall the power rule of exponents

https://www.qalaxia.com/viewDiscussion?messageId=5cdad460f32dc9584bdccec7

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

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

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}