Question

Calculati:

1) (√3+√2) ori √2

2) (√3-√4)(1+√2)

3) (3+ √2)(1+ √2)

4) (√8 + √2)(1+ √2)

5) (-√3+√2)(1+√2)

6) (√3 - √15)(1+ √5)

7) (2√3 - √2)(3-√2)

Answer 1

1

$( \sqrt{3} + \sqrt{2} ) \times \sqrt{2 = } \sqrt{3} \sqrt{2} + \sqrt{2} \sqrt{2} = \sqrt{6} + 2$

2

$( \sqrt{3} - \sqrt{4})(1 + \sqrt{2} ) = (\sqrt{3} - 2) \times (1 + \sqrt{2} ) = \sqrt{3} + \sqrt{6} - 2 - 2 \sqrt{2}$

3

$(3 + \sqrt{2} )(1 + \sqrt{2)} = 3 + 3 \sqrt{2} + \sqrt{2} + \sqrt{2} \sqrt{2} = 3 + 3 \sqrt{2} + \sqrt{2} + 2 = 5 + 4 \sqrt{2}$

4

$( \sqrt{8} + \sqrt{2} )(1 + \sqrt{2} ) = (2 \sqrt{2} + \sqrt{2} ) \times (1 + \sqrt{2} ) = 3 \sqrt{2} \times (1 + \sqrt{2}) = 3 \sqrt{2} + 6$

5

$( - \sqrt{3} + \sqrt{2} )(1 + \sqrt{2}) = - \sqrt{3} - \sqrt{3} \sqrt{2} + \sqrt{2} + \sqrt{2} \sqrt{2} = - \sqrt{3} - \sqrt{6} + \sqrt{2} + 2$

6

$( \sqrt{3} - \sqrt{15} )(1 + \sqrt{5} ) = \sqrt{3} + \sqrt{15} - \sqrt{15} - \sqrt{75} = \sqrt{3} - si \: acum \: e \: 5 \sqrt{3} = - 4 \sqrt{3}$

7

$(2 \sqrt{3} - \sqrt{2} )(3 - \sqrt{2} ) =2 \sqrt{3} \times 3 - 2 \sqrt{3} \sqrt{2} - 3 \sqrt{2} - \sqrt{2} \times ( - \sqrt{2} ) = 6 \sqrt{3} - 2 \sqrt{6} - 3 \sqrt{2} + 2$

Answer 2

Răspuns:

Explicație pas cu pas:

1)     (√3+√2) × √2  = √6 + √4 = 2 + √6

2)   (√3-√4) (1+√2)  = √3 - √4 + √6 - √8 = √3 - 2 + √6 - 2√2

3)    (3+ √2) (1+ √2)  = 3 + √2 + 3√2 + 2 = 5 + 4√2

4)   (√8 + √2 )(1+ √2)  = √8 + √2 + √16 + 2 = 2√2 + √2 + 4 + 2 = 3√2 + 6

5)   (-√3+√2) (1+√2)  = - √3 + √2 - √6 + 2

6)   (√3 - √15) (1+ √5)  = √3 - √15 + √15 - 5√3 = - 4√3

7)   (2√3 - √2) (3-√2) = 6√3 - 3√2 - 2√6 + 2