Question

Помогите, умоляю вас!!!

Answer 1

4)

$8 \sqrt{2} = \sqrt{ {8}^{2} \times 2} = \sqrt{64 \times 2} = \sqrt{128}$

$6 \sqrt{3} = \sqrt{ {6}^{2} \times 3} = \sqrt{36 \times 3} = \sqrt{108}$

$a \sqrt{2} = \sqrt{2a {}^{2} }$

5)

$\frac{1}{ \sqrt{5} } = \frac{ \sqrt{5} }{ \sqrt{5} \times \sqrt{5} } = \frac{ \sqrt{5} }{5}$

$\frac{1}{ \sqrt{a} } = \frac{ \sqrt{a} }{ \sqrt{a} \times \sqrt{a} } = \frac{ \sqrt{a} }{a}$

$\frac{5}{ \sqrt{10} } = \frac{5 \sqrt{10} }{ \sqrt{10} \times \sqrt{10} } = \frac{5 \sqrt{10} }{10} = \frac{ \sqrt{10} }{2}$

6)

$\sqrt{a} ( \sqrt{a} + \sqrt{b} ) - \sqrt{ab} = \\ a + \sqrt{ab} - \sqrt{ab} = a$

$(2 \sqrt{2} + 3 \sqrt{3} )(2 \sqrt{2} - 3 \sqrt{3} ) = \\ (2 \sqrt{2} ) {}^{2} - (3 \sqrt{3} ) {}^{2} = \\ 4 \times 2 - 9 \times 3 = 8 - 27 = - 19$