use the product property of roots to choose the expression equivalent to $\sqrt3{5x} \cdot \sqrt3{25x^2}$

* $\sqrt3{30x}$
* $\sqrt3{125x^3}$
* $\sqrt3{30x^2}$
* $\sqrt6{125x^3}$

simplify $\sqrt3{5x} \cdot \sqrt3{25x^2}$ completely.

* $25x^3$
* $25x$
* $5x^3$
* $5x$

Question

use the product property of roots to choose the expression equivalent to $\sqrt3{5x} \cdot \sqrt3{25x^2}$

* $\sqrt3{30x}$
* $\sqrt3{125x^3}$
* $\sqrt3{30x^2}$
* $\sqrt6{125x^3}$

simplify $\sqrt3{5x} \cdot \sqrt3{25x^2}$ completely.

* $25x^3$
* $25x$
* $5x^3$
* $5x$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Radical Simplification" ], "new_concepts": [ "Product Property of Radicals" ], "current_concepts": [ "Exponent Rules", "Radical Simplification", "Product Property of Radicals" ] } ## Apply the product property of roots Using the *Exponent Rules* knowledge point $$ \sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{5x \cdot 25x^2} = \sqrt[3]{125x^3} $$ ## Simplify the radicand Using the *Exponent Rules* and *Radical Simplification* knowledge points $$ \begin{aligned} 125x^3 &= 5^3 \cdot x^3 = (5x)^3\ \sqrt[3]{125x^3} &= \sqrt[3]{(5x)^3} = 5x \end{aligned} $$ ## Question 1 (A) $\sqrt[3]{30x}$

(B) $\sqrt[3]{125x^2}$

(C) $\sqrt[3]{30x^2}$

(D) $\sqrt[6]{125x^2}$ ## Question 2 (A) $25x^3$

(B) $25x$

(C) $5x^3$

(D) $5x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the product property of roots

Simplify the radicand

Answer:

Question 1

Question 2