Question

помогите пожалуйста! исключите иррациональность из знаменателя:

1) 6/квадратный корень из 7=

2) 2/квадратный корень из 8=

3) 5/квадратный корень из 12 - квадратный корень из 7 =

4) 15/квадратный корень из 11 + квадратный корень из 6 =

Answer 1

1) $frac{6}{sqrt{7}}=frac{6sqrt{7}}{(sqrt{7})^2}=frac{6sqrt{7}}{7}$

2) $frac{2}{sqrt{8}}=frac{2}{sqrt{4cdot2}}=frac{2}{2sqrt{2}}=frac{2sqrt{2}}{2(sqrt{2})^2}=frac{2sqrt{2}}{2cdot2}=frac{2sqrt{2}}{4}=frac{sqrt{2}}{2}$

3) $frac{5}{<var>sqrt{12}</var>-sqrt{7}}=frac{5(<var>sqrt{12}</var>+sqrt{7})}{(<var>sqrt{12}-</var>sqrt{7})<var>(<var>sqrt{12}+</var>sqrt{7})</var>}=<var>frac{5(<var>sqrt{12}</var>+sqrt{7})}{(<var>sqrt{12}</var>)^2-<var>(<var></var>sqrt{7})^2</var>}=<var><var>frac{5(<var>sqrt{12}</var>+sqrt{7})}{12-7<var></var>}=</var></var></var></var><var><var><var><var>frac{5(<var>sqrt{12}</var>+sqrt{7})}{5}</var></var></var></var>=<var><var><var><var><var>sqrt{12}</var>+sqrt{7}</var></var></var>$

4) $<var>frac{15}{<var>sqrt{11}</var>+sqrt{6}}=frac{15(<var>sqrt{11}</var>-sqrt{6})}{(<var>sqrt{11}+</var>sqrt{6})<var>(<var>sqrt{11}-</var>sqrt{6})</var>}=<var>frac{15(<var>sqrt{11}</var>-sqrt{6})}{(<var>sqrt{11}</var>)^2-<var>(<var></var>sqrt{6})^2</var>}=<var><var>frac{15(<var>sqrt{11}</var>-sqrt{6})}{11-6<var></var>}=</var></var></var></var><var><var><var><var>frac{15(<var>sqrt{11}</var>-sqrt{6})}{5}=3<var><var><var><var>(<var>sqrt{11}</var>-sqrt{6}</var></var></var></var></var></var></var></var>)$

Answer 2

1) $frac{6}{sqrt{7}}=frac{6}{sqrt{7}}cdotfrac{sqrt{7}}{sqrt{7}}=frac{6sqrt{7}}{7}$

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2) $frac{2}{sqrt{8}}=frac{2}{sqrt{4cdot2}}=frac{2}{2sqrt{2}}=frac{1}{sqrt{2}}= frac{1}{sqrt{2}}cdotfrac{sqrt{2}}{sqrt{2}}=frac{sqrt{2}}{2}$

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3) $frac{5}{sqrt{12}-sqrt{7}}=frac{5(sqrt{12}+sqrt{7})}{(sqrt{12}-sqrt{7})(sqrt{12}+sqrt{7})}= frac{5(sqrt{12}+sqrt{7})}{(sqrt{12})^2-(sqrt{7})^2}=frac{5(sqrt{12}+sqrt{7})}{12-7}=$

$frac{5(sqrt{12}+sqrt{7})}{5}=sqrt{12}+sqrt{7}$

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4) $frac{15}{sqrt{11}+sqrt{6}}=frac{15(sqrt{11}-sqrt{6})}{(sqrt{11}+sqrt{6})(sqrt{11}-sqrt{6})}=frac{15(sqrt{11}-sqrt{6})}{(sqrt{11})^2-(sqrt{6})^2}=frac{15(sqrt{11}-sqrt{6})}{11-6}=$

$frac{15(sqrt{11}-sqrt{6})}{5}=3(sqrt{11}-sqrt{6})=3sqrt{11}-3sqrt{6}$