simplify the radicals in the given expression: $8sqrt3{a^{4}b^{3}c^{2}} - 14absqrt3{ac^{2}}$…

simplify the radicals in the given expression: $8sqrt3{a^{4}b^{3}c^{2}} - 14absqrt3{ac^{2}}$ \n$8absqrt{ac^{2}} - 14absqrt3{ac^{2}}$ \n$8a^{2}bcsqrt3{b} - 14abcsqrt3{a}$ \n$8absqrt3{ac^{2}} - 14absqrt3{ac^{2}}$ \n$8a^{2}bcsqrt{b} - 14abcsqrt{a}$

simplify the radicals in the given expression: $8sqrt3{a^{4}b^{3}c^{2}} - 14absqrt3{ac^{2}}$ \n$8absqrt{ac^{2}} - 14absqrt3{ac^{2}}$ \n$8a^{2}bcsqrt3{b} - 14abcsqrt3{a}$ \n$8absqrt3{ac^{2}} - 14absqrt3{ac^{2}}$ \n$8a^{2}bcsqrt{b} - 14abcsqrt{a}$

Answer

Answer:

8a^{2}bc\sqrt[3]{b}-14abc\sqrt[3]{a}

Explanation:

Step1: Simplify first - radical term

8\sqrt[3]{a^{4}b^{3}c^{2}}=8\sqrt[3]{a^{3}\cdot a\cdot b^{3}\cdot c^{2}} = 8ab\sqrt[3]{ac^{2}}=8a^{2}bc\sqrt[3]{b}

Step2: Analyze second - radical term

  • 14ab\sqrt[3]{ac^{2}} cannot be further simplified in the context of combining with the first - term in a non - cube - root form. And we know that \sqrt[3]{ac^{2}} is part of the original expression. When we consider the simplified form of the first term in terms of cube - roots and the second term, the overall simplified form of 8\sqrt[3]{a^{4}b^{3}c^{2}}-14ab\sqrt[3]{ac^{2}} is 8a^{2}bc\sqrt[3]{b}-14abc\sqrt[3]{a}