Question

Vă rog frumos, să îmi faceți toate exercițiile. ​

Answer 1

Răspuns:

1

Explicație pas cu pas:

1 a.

$\sqrt{121} = \sqrt{ {11}^{2} } = 11$

b.

$\sqrt{225} = \sqrt{ {15}^{2} } = 15$

c.

$\sqrt{961} = \sqrt{ {31}^{2} } = 31$

D.

$\sqrt{9 \times 16} = \sqrt{ {3}^{2} \times {2}^{4} } = 3 \times {2}^{2} = 3 \times 4 = 12$

e.

$\sqrt{25 \times 81} = \sqrt{ {5}^{2} \times {9}^{2} } = 5 \times 9 = 45$

f.

$\sqrt{144 \times 361} = \sqrt{ {12}^{2} \times {19}^{2} } = 12 \times 19 = 228$

3.a.

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

b.

$- 2 \times \sqrt[3]{2} = - \sqrt[3]{ {2}^{3} \times 2} = \sqrt[3]{16}$

c.

$3 \times \sqrt{3} = \sqrt{ {3}^{2} \times 3 } = \sqrt{27}$

D.

$- 3 \sqrt{3} = - \sqrt{27}$

e.

$3 \times \sqrt[3]{3} = \sqrt[3]{ {3}^{3} \times 3} = \sqrt[3]{81}$

f.

$5 \times \sqrt[3]{2} = \sqrt[3]{ {5}^{3} \times 2 } = \sqrt[3]{250}$

2.a.

$\frac{2}{ \sqrt{6} } = \frac{2 \times \sqrt{6} }{ \sqrt{6} \times \sqrt{6} } = \frac{2 \sqrt{6} }{ \sqrt{ {6}^{2} } } = \frac{2 \sqrt{6} }{6} = \frac{ \sqrt{6} }{3}$

b.

$\frac{1}{ \sqrt[3]{2} } = \frac{ \sqrt[3]{ {2}^{2} } }{ \sqrt[3]{2} \times \sqrt[3]{ {2}^{2} } } = \frac{ \sqrt[3]{ {2}^{2} } }{ \sqrt[3]{ {2}^{3} } } = \frac{ \sqrt[3]{ {2}^{2} } }{2}$

c.

$\frac{1}{ \sqrt{3} - \sqrt{2} } = \frac{ \sqrt{3} + \sqrt{2} }{( \sqrt{3} - \sqrt{2)} \times ( \sqrt{3} + \sqrt{2)} } = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{ {3}^{2} } - \sqrt{ {2}^{2} } } = \frac{ \sqrt{3} + \sqrt{2} }{3 - 2} = \sqrt{3} + \sqrt{2}$

D.

$\frac{2}{ \sqrt{5} + \sqrt{3} } = \frac{2 \times ( \sqrt{5} - \sqrt{3}) }{5 - 3} =$