Express each one of the following with rational denominator : (i) 13+�

1.	Express each one of the following with rational denominator : (i) 13+√2 (ii) 1√6−√5 (iii) 16√41−5 (iv) 305√3−3√5 (v) 12√5+√3 (vi) 3√3+12√2−√3 (vii) 6−4√26+4√2 (viii) 3√2+12√5−3 (ix) b2√a2+b2+a
Answer» Express each one of the following with rational denominator : (i) $\frac{1}{3 + \sqrt{2}}$ (ii) $\frac{1}{\sqrt{6} - \sqrt{5}}$ (iii) $\frac{16}{\sqrt{41} - 5}$ (iv) $\frac{30}{5 \sqrt{3} - 3 \sqrt{5}}$ (v) $\frac{1}{2 \sqrt{5} + \sqrt{3}}$ (vi) $\frac{3 \sqrt{3} + 1}{2 \sqrt{2} - \sqrt{3}}$ (vii) $\frac{6 - 4 \sqrt{2}}{6 + 4 \sqrt{2}}$ (viii) $\frac{3 \sqrt{2} + 1}{2 \sqrt{5} - 3}$ (ix) $\frac{b^{2}}{\sqrt{a^{2} + b^{2} + a}}$

Express each one of the following with rational denominator : (i) 13+√2 (ii) 1√6−√5 (iii) 16√41−5 (iv) 305√3−3√5 (v) 12√5+√3 (vi) 3√3+12√2−√3 (vii) 6−4√26+4√2 (viii) 3√2+12√5−3 (ix) b2√a2+b2+a

Answer»

Express each one of the following with rational denominator :

(i) $\frac{1}{3 + \sqrt{2}}$

(ii) $\frac{1}{\sqrt{6} - \sqrt{5}}$

(iii) $\frac{16}{\sqrt{41} - 5}$

(iv) $\frac{30}{5 \sqrt{3} - 3 \sqrt{5}}$

(v) $\frac{1}{2 \sqrt{5} + \sqrt{3}}$

(vi) $\frac{3 \sqrt{3} + 1}{2 \sqrt{2} - \sqrt{3}}$

(vii) $\frac{6 - 4 \sqrt{2}}{6 + 4 \sqrt{2}}$

(viii) $\frac{3 \sqrt{2} + 1}{2 \sqrt{5} - 3}$

(ix) $\frac{b^{2}}{\sqrt{a^{2} + b^{2} + a}}$