Which one of the following are irrational numbers? (i) √(2 + √3) (ii) √(4 + √25) (iii) cube root of (5 + √7)

Question

Which one of the following are irrational numbers?

(i) \(\sqrt{2+\sqrt{3}}\)

(ii) \(\sqrt{4+\sqrt{25}}\)

(iii) \(\sqrt[3]{5+\sqrt{7}}\)

(iv) \(\sqrt{8-\sqrt[3]{8}}\)

(a) (ii), (iii) and (iv) 

(b) (i), (ii) and (iv) 

(c) (i), (ii) and (iii) 

(d) (i), (iii) and (iv)

Answer 1

(d) (ii), (iii) and (iv)

\(\sqrt{4+\sqrt{25}}\) = √9 = 3; \(\sqrt{8-\sqrt[3]{8}}\) = \(\sqrt{8-2}\) = \(\sqrt{6}\)