Question

if a = 7^1/2- 6^1/2 and b = 6^{1/2 -} 51/2, then
(a)a>b (b)a=b
(c)a<b

Answer 1

$$\begin{gathered} \mathrm{a}=\sqrt{7}-\sqrt{6} \\ \mathrm{b}=\sqrt{6}-\sqrt{5} \\ \mathrm{Squaring},\mathrm{we}\mathrm{get} \\ {\mathrm{a}}^2={\left(\sqrt{7}-\sqrt{6}\right)}^2=7+6-2\sqrt{42}=13-2\sqrt{42}=0.038 \\ \mathrm{a}=0.194 \\ {\mathrm{b}}^2={\left(\sqrt{6}-\sqrt{5}\right)}^2=6+5-2\sqrt{30}=11-2\sqrt{30}=0.045 \\ \mathrm{b}=0.213 \\ \mathrm{So}\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that}\mathrm{b}>\mathrm{a} \end{gathered}$$