Question

How can I find the exact distance between the points(√7,-√2)and (4√7,5√2)

Answer 1

`\bf d=\sqrt{[4√(7)-√(7)]^2~+~[5√(2)-(-√(2))]^2} \\\\\\ d=\sqrt{(4√(7)-√(7))^2~+~(5√(2)+√(2))^2}\implies d=\sqrt{(3√(7))^2~+~(6√(2))^2} \\\\\\ d=√(3^2\cdot 7~~+~~6^2\cdot 2)\implies d=√(63+72)\implies d=√(135) \\\\\\ \begin{cases} 135=5\cdot 3\cdot 3\cdot 3\\ \qquad 5\cdot 3^2\cdot 3\\ \qquad 15\cdot 3^2 \end{cases}\implies d=√(15\cdot 3^2)\implies d=3√(15)`