Question

Simplify the expression to the closest integer: $\frac{1}{3-\sqrt{2}}$

Answer 1

We rationalize the number as

,$\frac{1}{3-\sqrt{2}}\times \frac{3+\sqrt{2}}{3+\sqrt{2}}=\frac{3+\sqrt{2}}{9-2}=\frac{3+\sqrt{2}}{7}valueof\sqrt{2}\approx 1.414,=\frac{4.414}{7}=0.63$

Thus the closest integer to the value above is $1$.