Question

Rationalise the denominator and simplify. 5/root3-root2​

Answer 1

Answer:

5(√3+√2)/1

Step-by-step explanation:

5/√3-√2 ×√3+√2/√3+√2

5(√3+√2)/√3^2-√2^2

5(√3+√2)/1 answer

Answer 2

To rationalize:

$\sf \frac{5}{\sqrt{3}\ -\ \sqrt{2}}\\\\ Multiply\ both\ the\ numerator\ and\ the\ denominator\\ with\ (\sqrt{3}\ +\ \sqrt{2}),\ its\ inverse.\\\\\frac{5\ \times \ (\sqrt{3}\ +\ \sqrt{2})}{(\sqrt{3}\ -\ \sqrt{2})\ (\sqrt{3}\ +\ \sqrt{2})}\\\\\\ =\ \frac{5\ (\sqrt{3}\ +\ \sqrt{2})}{(\sqrt{3})^{2}\ -\ (\sqrt{2})^{2}}\\\\\\ =\ \frac{5\ (\sqrt{3}\ +\ \sqrt{2})}{3\ -\ 2}\\\\\\ =\ \frac{5\sqrt{3}\ + 5\sqrt{2}}{1}\\\\ Therefore,\ the\ new\ number\ is\ \frac{5\sqrt{3}\ + 5\sqrt{2}}{1}\ or\ 5\sqrt{3}\ + 5\sqrt{2}.$