Simplify the following using addition and subtraction properties of surds: (i) 5√3 + 18√3 - 2√3 (ii) 4 3√5 + 2 2√5 - 3 3√5

Question

Simplify the following using addition and subtraction properties of surds:

(i) \(5\sqrt{3}+18\sqrt{3}-2\sqrt{3}\)

(ii) \(4\sqrt[3]{5}+2\sqrt[2]{5}-3\sqrt[3]{5}\)

(iii) \(3\sqrt{75}+5\sqrt{48}-\sqrt{243}\)

(iv) \(5\sqrt[3]{40}+2\sqrt[3]{625}-3\sqrt[3]{320}\)

Answer 1

(i) \(5\sqrt{3}+18\sqrt{3}-2\sqrt{3}\) = (5 + 18 - 2)√3 = 21√3

(ii) \(4\sqrt[3]{5}+2\sqrt[2]{5}-3\sqrt[3]{5}\) = (4 + 2 - 3) \(\sqrt[3]{5}\) = 3 \(\sqrt[3]{5}\)

(iii) \(3\sqrt{75}+5\sqrt{48}-\sqrt{243}\)

(iv) \(5\sqrt[3]{40}+2\sqrt[3]{625}-3\sqrt[3]{320}\)