Question

Perform the indicated operations. Assume all variables represent positive real numbers. ﻿372m2−532m2−318m23\sqrt{$$72m^2$$} - 5\sqrt{$$32m^2$$} - 3\sqrt{$$18m^2$$}
372m2​−532m2​−318m2​

Accepted Answer

Start by expressing each radical term in the form of $$ \sqrt[3]{a \cdot b} $$, where $$a is a $$perfect cube and $$b is $$the remaining factor. For example, rewrite $$ \sqrt[3]{72m^2}  as$$ $$ \sqrt[3]{	ext{(perfect cube)} 	imes 	ext{(other factor)}} . $$Identify the perfect cube factors inside each cube root. For instance, since $$72 = 8 	imes 9$$ and $$8 is a $$perfect cube ($$2^3$$), rewrite $$ \sqrt[3]{72m^2}  as$$ $$ \sqrt[3]{8 	imes 9m^2} . Do $$the same for the other terms: $$ \sqrt[3]{32m^2} $$ and $$ \sqrt[3]{18m^2} . $$Use the property of cube roots that $$ \sqrt[3]{a 	imes b} = \sqrt[3]{a} 	imes \sqrt[3]{b}  to $$separate the perfect cube and the remaining factor. For example, $$ \sqrt[3]{8 	imes 9m^2} = \sqrt[3]{8} 	imes \sqrt[3]{9m^2} . $$Simplify the cube roots of the perfect cubes. Since $$ \sqrt[3]{8} = 2 $$, $$ \sqrt[3]{27} = 3 $$, and so on, replace these with their simplified values. This will allow you to rewrite each term as a product of a constant and a cube root of the remaining factor. After simplifying each term, combine like terms by subtracting or adding the coefficients of the cube roots that have the same radicand (the expression inside the cube root). This will give you the simplified expression for the original problem.

Perform the indicated operations. Assume all variables represent positive real numbers. $3\(\sqrt{72m^2}\) - 5\(\sqrt{32m^2}\) - 3\(\sqrt{18m^2}\)$

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Simplifying Radicals

Like Radicals and Combining Terms

Operations with Variables under Radicals

Perform the indicated operations. Assume all variables represent positive real numbers. 372m2−532m2−318m23\(\sqrt{72m^2}\) - 5\(\sqrt{32m^2}\) - 3\(\sqrt{18m^2}\) 372m2−532m2−318m2