what is the following sum?\n4(\\sqrt5{x^{2}y})+3(\\sqrt5{x^{2}y})\n\\(7(\\sqrt10{x^{2}y})\\)\n\\(7(\\sqrt10{x…

what is the following sum?\n4(\\sqrt5{x^{2}y})+3(\\sqrt5{x^{2}y})\n\\(7(\\sqrt10{x^{2}y})\\)\n\\(7(\\sqrt10{x^{4}y^{2}})\\)\n\\(7(\\sqrt5{x^{2}y})\\)\n\\(7(\\sqrt5{x^{4}y^{2}})\\)

what is the following sum?\n4(\\sqrt5{x^{2}y})+3(\\sqrt5{x^{2}y})\n\\(7(\\sqrt10{x^{2}y})\\)\n\\(7(\\sqrt10{x^{4}y^{2}})\\)\n\\(7(\\sqrt5{x^{2}y})\\)\n\\(7(\\sqrt5{x^{4}y^{2}})\\)

Answer

Explanation:

Step1: Combine like - terms

Since (4\sqrt[5]{x^{2}y}) and (3\sqrt[5]{x^{2}y}) are like - terms, we use the distributive property (a\times c + b\times c=(a + b)\times c). Here (a = 4), (b = 3), and (c=\sqrt[5]{x^{2}y}). So (4\sqrt[5]{x^{2}y}+3\sqrt[5]{x^{2}y}=(4 + 3)\sqrt[5]{x^{2}y}).

Step2: Calculate the coefficient

(4+3 = 7), so the sum is (7\sqrt[5]{x^{2}y}).

Answer:

(7\left(\sqrt[5]{x^{2}y}\right))