Question

помогите пожалуйста с заданиями:)

Answer 1

$5sqrt{21}+sqrt{frac{3}{7}}-9sqrt{frac{7}{3}}=frac{5sqrt{21}*sqrt{21}+sqrt{3}*sqrt{3}-9sqrt{7}*sqrt{7}}{sqrt{21}}=frac{5*21+3-9*7}{sqrt{21}}=frac{45}{sqrt{21}}=frac{15sqrt{21}}{7}$

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

$frac{8+2sqrt{15}}{sqrt{3}+sqrt{5}}=frac{(8+2sqrt{15})(sqrt{3}-sqrt{5})}{(sqrt{3}+sqrt{5})(sqrt{3}-sqrt{5})}=frac{(2sqrt{45}-2sqrt{75}+8sqrt{3}-8sqrt{5})}{3-5}=frac{(6sqrt{5}-10sqrt{3}+8sqrt{3}-8sqrt{5})}{3-5}=frac{-2sqrt{5}-2sqrt{3}}{-2}=sqrt{5}+sqrt{3}$

$frac{7a-9b}{sqrt{7a}+3sqrt{b}}=frac{(sqrt{7a}+3sqrt{b})(sqrt{7a}-3sqrt{b})}{sqrt{7a}+3sqrt{b}}=sqrt{7a}-3sqrt{b}$

$frac{sqrt{a^4b^2+2a^3b^3+a^2b^4}}{sqrt{(a-b)(a^2-b^2)}}-frac{sqrt{a^3b^2+a^2b^3-1}}{(sqrt{a}-sqrt{b})(sqrt{a}+sqrt{b})}=frac{sqrt{a^2b^2(a^2+2ab+b^2)}}{sqrt{(a-b)(a-b)(a+b)}}-frac{sqrt{a^2b^2(a+b)-1}}{(sqrt{a})^2-(sqrt{b})^2}=frac{ab(a+b)}{(a-b)sqrt{a+b}}-frac{sqrt{(absqrt{a+b}-1)(absqrt{a+b}+1)}}{a-b}}=frac{absqrt{a+b}-sqrt{(absqrt{a+b}-1)(absqrt{a+b}+1)}}{a-b}=frac{absqrt{a+b}-sqrt{a^2b^2(a+b)-1}}{a-b}$

$sqrt{9+4sqrt{2}}-sqrt{9-4sqrt{2}}=sqrt{1^2+2*1*2sqrt{2}+(2sqrt{2})^2}-sqrt{1^2-2*1*2sqrt{2}+(2sqrt{2})^2}=sqrt{(1+2sqrt{2})^2}-sqrt{(1-2sqrt{2})^2}=1+2sqrt{2}+1-2sqrt{2}=2$