Question

COMO POSSO RESPONDER AS SEGUINTES PERGUNTAS?(URGENTE)​

Answer 1

1.a)

$- \sqrt{252} + \sqrt{28} = - 6 \sqrt{7} + 2 \sqrt{7} = - 4 \sqrt{7}$

b)

$\sqrt{96} + \sqrt{11} - 3\sqrt{112} = \\ 4 \sqrt{6} + \sqrt{11} - 3 \times 4 \sqrt{7} = \\ 4 \sqrt{6} + \sqrt{11} - 12 \sqrt{7} = \\ - 7 \sqrt{6 + 11 - 7} = - 7 \sqrt{10}$

2.a)

$\sqrt[5]{ {x}^{16} } \div \sqrt[5]{ {x}^{3} } = \\ {x}^{ \frac{16}{5} } \div {x}^{ \frac{3}{5} } = \\ \\ {x}^{ \frac{16}{5} - \frac{3}{5} } = {x}^{ \frac{16 - 3}{5} } = {x}^{ \frac{13}{5} }$

b)

$\frac{ \sqrt{480 {a}^{3} } }{ \sqrt{12 {a}^{2} } } = \frac{ \sqrt{ {2}^{2} \times {2}^{2} \times 30 {a}^{3} } }{ \sqrt{ {2}^{2} \times 3 {a}^{2} } } = \\ \\ 30 {a}^{3} = 30(a \times {a}^{2}) = 30a \times 30 {a}^{2} \\ \\ \frac{ \sqrt{ {2}^{2} \times {2}^{2} \times 30a \times 30 {a}^{2} } }{ \sqrt{ {2}^{2} \times 3 {a}^{2} } } = \\ \\ \frac{2 \times 2 \times 30a \sqrt{30a} }{2 \times 3a} = \\ \\ \frac{120a \sqrt{30a} }{6a} = 20a \sqrt{30a}$

3.a)

$a \: = \: b \: \times h \\ \\ a = \sqrt{42} \times \sqrt{18} \\ a = \sqrt{756} \\ a = \sqrt{ {2}^{2} \times {3}^{2} \times 3 \times 7} \\ a = 2 \times 3 \sqrt{3 \times 7} \\ a = 6 \sqrt{21}$

b)

$a = \frac{b \times h}{2} \\ \\ a = \frac{ \sqrt[3]{96} \times \sqrt[3]{54} }{2} \\ a = \frac{ \sqrt[3]{ {2}^{3} \times 12 } \times \sqrt[3]{2 \times {3}^{3} } }{2} \\ a = \frac{2 \sqrt[3]{12} \times3 \sqrt[3]{2} }{2} \\ a = \frac{6 \sqrt[3]{24} }{2} \\ a = \frac{6 \times 2 \sqrt[3]{3} }{2} \\ a = \frac{12 \sqrt[3]{3} }{2} \\ \\ a = 6 \sqrt[3]{3}$

4.

$\sqrt{5 + \sqrt{5} } \times \sqrt{5 - \sqrt{5} } = \\ \sqrt{25 - \sqrt{25} } = 5 - \sqrt{5}$