Question

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Answer 1

Explicație pas cu pas:

11.

$\sqrt{4 \sqrt{25} + {5}^{2} \cdot7 } = \sqrt{4\cdot 5 + 25 \cdot7 } = \sqrt{20 + 175} \\ = \sqrt{195} = \sqrt{3\cdot5\cdot13}$

$\sqrt{ {3}^{3}\cdot 4 - {3}^{3} + 9 \sqrt{9} } = \sqrt{ {3}^{3}\cdot {2}^{2} - {3}^{3} + {3}^{2}\cdot 3} \\ = \sqrt{ {3}^{3}\cdot {2}^{2} - {3}^{3} + {3}^{3}} = \sqrt{ {3}^{3}\cdot {2}^{2} } = 2 \cdot 3 \sqrt{3} = 6 \sqrt{3}$

$\sqrt{ \sqrt{225} + 6 \sqrt{36} + {5}^{3}} = \sqrt{15 + 6 \cdot 6 + 125} \\ = \sqrt{140 + 36} = \sqrt{176} = \sqrt{ {2}^{4}\cdot 11 } \\ = {2}^{2} \sqrt{11} = 4 \sqrt{11}$

12.a)

$\sqrt{12 \cdot x} = \sqrt{ {2}^{2}\cdot 3 \cdot x} = 2 \sqrt{3\cdot x} \\ = > x = 3$

12.b)

$\sqrt{48 \cdot x} = \sqrt{ {2}^{4}\cdot 3 \cdot x} = {2}^{2} \sqrt{3\cdot x} \\ = > x = 3$

1.a)

$P = 4 \cdot l = 4 \sqrt{5}\: cm \\ A = {l}^{2} = {( \sqrt{5} )}^{2} = 5 \: {cm}^{2}$

1.b)

$P = 3 \cdot l = 3 \cdot 2 \sqrt{3} = 6 \sqrt{3} \: cm \\ A = \frac{ {l}^{2} \sqrt{3}}{4} = \frac{({2 \sqrt{3}) }^{2}\cdot \sqrt{3} }{4} \\ = \frac{12\cdot \sqrt{3} }{4} =3 \sqrt{3} \: {dm}^{2}$