[tex]a = 1 + {2}^{0} + {2}^{1} + {2}^{2} + ... + {2}^{28} + {2}^{29} [/tex]
[tex]2a = 2 + {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{29} + {2}^{30} [/tex]
[tex]2a - a = 2 + {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{29} + {2}^{30} - 1 - {2}^{0} - {2}^{1} - {2}^{2} - ... - {2}^{28} - {2}^{29} [/tex]
[tex]a = 2 + {2}^{30} - 1 - 1 = 2 + {2}^{30} - 2 = {2}^{30} [/tex]
[tex] \sqrt{a} = \sqrt{{2}^{30} } = \sqrt{ {( {2}^{15} )}^{2} } = {2}^{15} [/tex]
