n- darajali ildiz. Ratsional ko‘rsatkichli daraja mavzusidan test savollari

Soddalashtiring:

\frac{27a+1}{9a^{\frac{2}{3}}-3\sqrt[3]{a}+1}-\frac{27a-1}{9\sqrt[3]{a^{2}}+3a^{\frac{1}{3}}+1}

\frac{1}{243} sonini 9 asosli daraja shaklida ifodalang.

Eng katta son berilgan javobni toping.

Eng katta sonni toping.

Hisoblang:

\frac{15^{\frac{2}{3}}\cdot 3^{\frac{1}{3}}}{5^{-\frac{1}{3}}}

Soddalashtiring:

\frac{a^{\frac{2}{3}}\cdot b^{\frac{2}{3}}\cdot ((ab)^{-\frac{1}{6}})^{4}}{(ab)^{-\frac{8}{3}}}

Hisoblang:

\frac{(\frac{1}{49})^{-\frac{1}{2}}-(\frac{1}{8})^{-\frac{1}{3}}}{64^{\frac{2}{3}}}

Hisoblang:

\frac{30^{\frac{1}{3}}\cdot 3^{\frac{2}{3}}}{10^{-\frac{2}{3}}}

Hisoblang:

\lbrack 65\cdot (4^{\frac{1}{4}})^{-12}+\frac{2^{-5}}{-2}\rbrack ^{-1}

Hisoblang:

0.027^{-\frac{1}{3}}-(-\frac{1}{6})^{-2}+256^{\frac{3}{4}}-3^{-1}+5.5^{0}

Agar n=81 bo‘lsa, \sqrt[3]{n\sqrt{n}} qiymati qanchaga teng bo‘ladi?

Hisoblang:

\frac{\sqrt[3]{-24}+\sqrt[3]{81}+\sqrt[3]{192}}{\sqrt[3]{-375}}

Hisoblang:

\sqrt{3\cdot \sqrt[3]{81}}\cdot \sqrt[6]{96}

Hisoblang:

\sqrt[7]{243\cdot 81^{2}\cdot 9^{4}}

Sonlarni o‘sish tartibida joylashtiring:

1; \sqrt{2}; \sqrt[3]{3}; \sqrt[4]{4}

Hisoblang:

\lbrack (\frac{1}{33})^{-1}\cdot (\sqrt[4]{4})^{-12}+\frac{2^{-5}}{-2}\rbrack ^{-1}

Sonlardan qaysilari irratsional sonlar?

m=\sqrt[4]{256}, \pi =3.141516_\cdots,

p=\sqrt{\sqrt{\sqrt{81}}+13}, q=\frac{1}{\sqrt{2}}

Ushbu sonlardan qaysilari irratsional sonlar hisoblanadi?

m=\sqrt[4]{2.56}, n=3.4(25),

p=3.142_\cdots , q=\sqrt{\sqrt{\sqrt{16}}+2} 

Hisoblang:

\sqrt[3]{2\sqrt{6}-5}\cdot \sqrt[6]{49+20\sqrt{6}}

Hisoblang:

\sqrt[3]{9+\sqrt{73}}\cdot \sqrt[3]{9-\sqrt{73}}

Soddalashtiring:

\sqrt{2\sqrt{2}-1}\cdot \sqrt[4]{9+4\sqrt{2}}

Hisoblang:

\sqrt{3-2\sqrt{2}}\cdot \sqrt[4]{17+12\sqrt{2}}

Soddalashtiring:

\sqrt[3]{80+48\sqrt{3}}

Hisoblang:

(\sqrt[6]{9+4\sqrt{5}}+\sqrt[3]{\sqrt{5}+2})\cdot \sqrt[3]{\sqrt{5}-2}

Soddalashtiring:

\sqrt[4]{97+56\sqrt{3}}

Hisoblang:

\sqrt[2]{216\cdot 512}+\sqrt[5]{32\cdot 243}

Hisoblang:

\frac{\sqrt[4]{3+2\sqrt{2}}}{\sqrt{\sqrt{2}+1}}

Hisoblang:

\sqrt[3]{2-\sqrt{3}}\cdot \sqrt[6]{7+4\sqrt{3}}

Hisoblang:

\sqrt[6]{3-2\sqrt{2}}:\sqrt[3]{\sqrt{2}-1}

Ifodani hisoblang:

\sqrt[4]{\frac{4.1^{3}-2.15^{3}}{1.95}+4.1\cdot 2.15}