In each of the following determine rational numbers a and b : (i) √3

1.	In each of the following determine rational numbers a and b : (i) √3−1√3+1=a−b√3 (ii) 4+√22+√2=a−√b (iii) 3+√23−√2=a+b√2 (iv) 5+3√37+4√3=a+b√3 (v) √11−√7√11+√7=a−b√77 (vi) 4+3√54−3√5=a+b√5
Answer» In each of the following determine rational numbers a and b : (i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$ (ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$ (iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$ (iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$ (v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$ (vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$

In each of the following determine rational numbers a and b : (i) √3−1√3+1=a−b√3 (ii) 4+√22+√2=a−√b (iii) 3+√23−√2=a+b√2 (iv) 5+3√37+4√3=a+b√3 (v) √11−√7√11+√7=a−b√77 (vi) 4+3√54−3√5=a+b√5

Answer»

In each of the following determine rational numbers a and b :

(i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$

(ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$

(iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$

(iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

(v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$

(vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$