Question

Calculand valoarea numarul real a=√2^4+√2^7 se obtine

Answer 1

√2⁴=2²=4
√2⁷=√(2⁶x2)=2³x√2
4+8√2=4(1+2√2)

Answer 2

$a=\sqrt{2^4}+\sqrt{2^7} \\ \\ a = \sqrt{2^{2+2}}+\sqrt{2^{2+2+2+1}} \\ \\ a = \sqrt{2^2\cdot 2^2} +\sqrt{2^2\cdot 2^2\cdot 2^2\cdot 2} \\ \\ a = \sqrt{2^2}\cdot \sqrt{2^2}+\sqrt{2^2}\cdot \sqrt{2^2}\cdot \sqrt{2^2}\cdot \sqrt2 \\ \\ a = 2\cdot 2+2\cdot2\cdot2\cdot \sqrt2 \\ \\ a = 4+8\sqrt2$