Podcast
Questions and Answers
Evaluate (\sqrt[3]{-0.000000125})
Evaluate (\sqrt[3]{-0.000000125})
-0.05
Evaluate (\sqrt[3]{\frac{24}{81}}) as a fraction in lowest terms.
Evaluate (\sqrt[3]{\frac{24}{81}}) as a fraction in lowest terms.
(\frac{2}{3})
Evaluate (\sqrt{\frac{48}{75}}) as a fraction in lowest terms.
Evaluate (\sqrt{\frac{48}{75}}) as a fraction in lowest terms.
(\frac{4\sqrt{3}}{5})
Write (\sqrt{384}) as a mixed radical in simplest terms.
Write (\sqrt{384}) as a mixed radical in simplest terms.
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Write (\sqrt[4]{2560}) as a mixed radical in simplest terms.
Write (\sqrt[4]{2560}) as a mixed radical in simplest terms.
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Write (-4\sqrt{6}) as an entire radical.
Write (-4\sqrt{6}) as an entire radical.
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Write (-2\sqrt[5]{-6}) as an entire radical.
Write (-2\sqrt[5]{-6}) as an entire radical.
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Write (\left(0.1296\right)^{\frac{3}{4}}) as a radical, then evaluate.
Write (\left(0.1296\right)^{\frac{3}{4}}) as a radical, then evaluate.
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Write (\left(\frac{6}{48}\right)^{\frac{2}{3}}) as a radical, then evaluate.
Write (\left(\frac{6}{48}\right)^{\frac{2}{3}}) as a radical, then evaluate.
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Write (\left(\frac{486}{64}\right)^{0.2}) as a radical, then evaluate.
Write (\left(\frac{486}{64}\right)^{0.2}) as a radical, then evaluate.
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Write (\left(\sqrt[4]{\frac{1}{36}}\right)^{3}) as a power with a rational exponent.
Write (\left(\sqrt[4]{\frac{1}{36}}\right)^{3}) as a power with a rational exponent.
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Write (-\left(\frac{5}{7}\right)^{-\frac{7}{2}}) with a positive rational exponent.
Write (-\left(\frac{5}{7}\right)^{-\frac{7}{2}}) with a positive rational exponent.
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Evaluate (\left(81
ight)^{-\frac{3}{4}}) without using a calculator.
Evaluate (\left(81 ight)^{-\frac{3}{4}}) without using a calculator.
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Study Notes
Classification of Real Numbers and Radicals
- Real numbers can be classified into various categories such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
- Radicals involve roots of numbers, including square roots (√) and cube roots (∛).
- Evaluating square and cube roots can often reveal exact values or simplified forms.
Evaluating Radicals
- For the expression ( \sqrt[3]{-\frac{24}{81}} ), simplify to find its value in fractional form.
- The expression ( -\sqrt{\frac{48}{75}} ) should also be evaluated and expressed in lowest terms.
Converting Between Mixed and Entire Radicals
- Mixed radicals contain a whole number and a radical part, whereas entire radicals have no whole number.
- Example of conversion: ( \sqrt{384} ) can be expressed as a mixed radical.
- An expression such as ( -\sqrt[4]{2560} ) could also be converted into mixed radical form.
Simplifying Radicals
- The expression ( -4\sqrt{6} ) is presented as an entire radical and should be in simplest terms.
- ( -2\sqrt[5]{-6} ) is another example that should be simplified and expressed as an entire radical.
Powers with Positive Rational Exponents
- Positive rational exponents can be expressed in radical form, e.g., ( \left(0.1296\right)^{\frac{3}{4}} ).
- Evaluation of such powers involves converting to radicals and determining their value.
Writing Radicals as Powers
- Radicals can be expressed using rational exponents, exemplified by ( \left( \sqrt[4]{\frac{1}{36}} \right)^{3} ).
Powers with Negative Rational Exponents
- Negative rational exponents indicate reciprocal operations, e.g., ( -\left( \frac{5}{7} \right)^{- \frac{7}{2}} ) can be written with a positive exponent by taking the reciprocal.
- Evaluating powers such as ( \left( 81 \right)^{- \frac{3}{4}} ) requires recognizing the base and the effect of the negative exponent.
Self-Assessment
- Assess proficiency in evaluating radicals, converting between forms, and understanding rational exponents.
- Improvement areas can involve practicing radical simplification, understanding exponent rules, and gaining confidence in evaluations without technology.
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Description
This quiz assesses your understanding of classifying real numbers and evaluating square and cube roots without the use of technology. You will solve problems involving radicals and express your answers as simplified fractions.
