Question

27. Folosind algoritmul de extragere a rădăcinii pătrate, calculați: b) √7225; √2209; a) √√3721; √1936; √4624; √√9216; c) √√2116; √√3481; √3844; √2916; d) √12769; √7056; √3969; √√45369; √15129; √15876.​

Answer 1

Explicație pas cu pas:

26.

$\sqrt{576} = \sqrt{ {2}^{6} \times {3}^{2} } = {2}^{3} \times 3 = 24$

$\sqrt{729} = \sqrt{ {3}^{6} } = {3}^{3} = 27$

$\sqrt{625} = \sqrt{ {5}^{4} } = {5}^{2} = 25$

$\sqrt{324} = \sqrt{ {2}^{2} \times {3}^{4} } = 2 \times {3}^{2} = 18$

$\sqrt{400} = \sqrt{ {2}^{4} \times {5}^{2} } = {2}^{2} \times 5 = 20$

$\sqrt{784} = \sqrt{ {2}^{4} \times {7}^{2} } = {2}^{2} \times 7 = 28$

$\sqrt{441} = \sqrt{ {3}^{2} \times {7}^{2} } = 3 \times 7 = 21$

$\sqrt{676} = \sqrt{ {2}^{2} \times {13}^{2} } = 2 \times 13 = 26$

$\sqrt{1600} = \sqrt{ {2}^{6} \times {5}^{2} } = {2}^{3} \times 5 = 40$

$\sqrt{1296} = \sqrt{ {2}^{4} \times {3}^{4} } = {2}^{2} \times {3}^{2} = 36$

$\sqrt{1764} = \sqrt{ {2}^{2} \times {3}^{2} \times {7}^{2} } = 2 \times 3 \times 7 = 42$

$\sqrt{2025} = \sqrt{ {3}^{4} \times {5}^{2} } = {3}^{2} \times 5 = 45$

$\sqrt{2500} = \sqrt{ {2}^{2} \times {5}^{4} } = 2 \times {5}^{2} = 50$

$\sqrt{2304} = \sqrt{ {2}^{8} \times {3}^{2} } = {2}^{4} \times 3 = 48$

$\sqrt{3136} = \sqrt{ {2}^{6} \times {7}^{2} } = {2}^{3} \times 7 = 56$

$\sqrt{5184} = \sqrt{ {2}^{6} \times {3}^{4} } = {2}^{3} \times {3}^{2} = 72$