Question

Simplify : $(5\sqrt{5}-5\sqrt{2})(\sqrt{5}+3\sqrt{2})$

• A. $5(2\sqrt{10}+1)$
• B. $5(3\sqrt{10}-2)$
• C. $5(2\sqrt{10}-1)$
• D. $2(5\sqrt{10}-1)$

Answer 1

The correct option is C $5(2\sqrt{10}-1)$

The given expression $(5\sqrt{5}-5\sqrt{2})+(\sqrt{5}+3\sqrt{2})$ can be simplified as shown below:

$(5\sqrt{5}-5\sqrt{2})(\sqrt{5}+3\sqrt{2})=\left[\right(5\sqrt{5}\times \sqrt{5})+(5\sqrt{5}\times 3\sqrt{2})+(-5\sqrt{2}\times \sqrt{5})+(-5\sqrt{2}\times 3\sqrt{2}\left)\right]=\left[\right(5\times 5)+(5\times 3\sqrt{10})+(-5\sqrt{10})+(-15\times 2\left)\right]=25+15\sqrt{10}-5\sqrt{10}-30=10\sqrt{10}-5=5(2\sqrt{10}-1)$

Hence, $(5\sqrt{5}-5\sqrt{2})(\sqrt{5}+3\sqrt{2})=5(2\sqrt{10}-1)$