Question

Cómo racionaliza está operación?

√1250 + √5000 - 17√2

Answer 1

$\sqrt{1250} + \sqrt{5000}-17 \sqrt{2}=\\ \sqrt{25\cdot50}+ \sqrt{50\cdot100}-17 \sqrt{2}=\\ \sqrt{25\cdot25\cdot 2}+ \sqrt{2\cdot25\cdot100}-17 \sqrt{2}=\\ \sqrt{25}\cdot \sqrt{25}\cdot \sqrt{2} + \sqrt{100} \cdot \sqrt{25}\cdot \sqrt{2} -17 \sqrt{2} =\\5\cdot5 \sqrt{2}+10\cdot5 \sqrt{2}-17 \sqrt{2}=\\25 \sqrt{2} +50 \sqrt{2}-17 \sqrt{2}=\\(25+50-17) \sqrt{2}=58 \sqrt{2}$