Question

помогитееее !!!!!!!!!!!!!!

Answer 1

1

$11sqrt{5} +sqrt{500}-sqrt{180}=11sqrt{5}+sqrt{100 times 5} -sqrt{36 times 5} =\11sqrt{5}+10sqrt{5} -6sqrt{5}=15sqrt{5}$

2

$3sqrt{2}(5sqrt{2}-sqrt{32})=3*5sqrt{2times 2}-3sqrt{2times 16 times 2}=15times 2-3times 4times 2=\30-24=6$

3

$(sqrt{6}+sqrt{3})^2=6+2sqrt{6times 3}+3=9+2sqrt{3times 3times 2}=9+6sqrt{2}$

4

$(sqrt{3}-sqrt{8})(sqrt{8}+sqrt{3})=(sqrt{3}-sqrt{8})(sqrt{3}+sqrt{8})=3-8=-5$

5

$frac{7+sqrt{7}}{5sqrt{7}} =frac{(7+sqrt{7})times sqrt{7}}{5sqrt{7}times sqrt{7}}=frac{7sqrt{7} + 7}{5times 7}=frac{7+7sqrt{7}}{35}$

6

$frac{10}{3-sqrt{5}}=frac{10(3+sqrt{5})}{(3-sqrt{5})(3+sqrt{5})}=frac{30+10sqrt{5}}{9-5}=frac{30+10sqrt{5}}{4}=7,5+2,5sqrt{5}$

7

$sqrt{12+6sqrt{3}}=sqrt{3^2+6sqrt{3}+(sqrt{3})^2}=sqrt{(3+sqrt{3})^2}=3+sqrt{3}$

Answer 2

Если что-то непонятно или где-то необходимы дополнительные объяснения, спрашивайте.

Answer 3

1)11√5+√500-√180=11√5+√(100.5)-√(36.5)=11√5+10√5-6√5=15√5

2)3√2(5√2-√32)=3√2(5√2-√(16.2))=3√2(5√2-4√2)=

 = 3√2√2=3.2=6

3)(√6+√3)²=(√6)²+2√6√3+(√3)²=6+2√18+3=9+2√(9.2)=

 =9+6√2

4)(√3-√8)(√8+√3)=(√3)²-(√8)²=3-8=-5

5)(7+√7)/5√7=(7+√7)√7/5√7√7=(7√7+7)/(5.7)=7(√7+1)/(5.7)=(√7+1)/5

6)10/(3-√5)=10(3+√5)/((3-√5)(3+√5)=10(3+√5)/(9-5)=

 = 10(3+√5)/4=2,5(3+√5)

7)√(12+6√3)=√(9+3+6√3)=√(9+6√3+3)=√(3²+2.3.√3+(√3)²)=

=√(3+√3)²=3+√3

(A²+2AB+B²=(A+B)²)