{"@context":"https://schema.org/","@type":"Quiz","name":"

If a and c are positive numbers, which of the following is equivalent to $\\sqrt{(a+c)^{3}}\\cdot\\sqrt{a+c}$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-181"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

If a and c are positive numbers, which of the following is equivalent to $\\sqrt{(a+c)^{3}}\\cdot\\sqrt{a+c}$?

","comment":{"@type":"Comment","text":"

Choice C is correct. Using the property that $\\sqrt{x}\\sqrt{y}=\\sqrt{xy}$ for positive numbers $x$ and $y$, with $x=\\left(a+c\\right)^{3}$ and $y = a + c$, it follows that $\\sqrt{\\left(a+c\\right)^{3}}\\cdot\\sqrt{a+c}=\\sqrt{\\left(a+c\\right)^{4}}$. By rewriting $\\left(a+c\\right)^{4}$ as $\\left(\\left(a+c\\right)^{2}\\right)^{2}$, it is possible to simplify the square root expression as follows: $\\sqrt{\\left(\\left(a+c\\right)^{2}\\right)^{2}}=\\left(a+c\\right)^{2}=a^{2}+2ac+c^ {2}$.

Choice A is incorrect and may be the result of $\\sqrt{\\left(a+c\\right)^{3}}+\\sqrt{\\left(a+c\\right)}$. Choice B is incorrect and may be the result of incorrectly rewriting $\\left(a+c\\right)^{2}$ as a $a^{2}+c^{2}$. Choice D is incorrect and may be the result of incorrectly applyingproperties of exponents.

"},"encodingFormat":"text/markdown","text":"

If a and c are positive numbers, which of the following is equivalent to $\\sqrt{(a+c)^{3}}\\cdot\\sqrt{a+c}$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$a+c$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$a^{2}+c^{2}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$a^{2}c^{2}$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$a^{2}+2ac+c^{2}$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-181"}

If a and c are positive numbers, which of the following is equivalent to $\sqrt{(a+c)^{3}}\cdot\sqrt{a+c}$?