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Radical Expressions and Equations

Multiple Radicals



83×644÷2. \sqrt[3]{8} \times \sqrt[4]{64} \div \sqrt{2}.

What is the value of bb that satisfies a15a17×aa157×a17a125=ab?\sqrt{\frac{a^{\frac{1}{5}}}{a^{\frac{1}{7}}}} \times \sqrt[7]{\frac{a}{a^{\frac{1}{5}}}} \times \sqrt[5]{\frac{a^{\frac{1}{7}}}{a^{\frac{1}{2}}}}=\sqrt[b]{a}?

Details and assumptions

bb is the index of the root on the right hand side.

What is the value of (13+169)(10100) \left(13 + \sqrt{-169}\right)\left(10 - \sqrt{-100}\right) ?

If x=10+1273+101273,x=\sqrt[3]{10+\sqrt{127}}+\sqrt[3]{10-\sqrt{127}}, what is the value of x3+9x?x^3+9x ?


20+291. \sqrt{20 + 2\sqrt{91}}.


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