Solving the Fifth Root of 32/243
The question asks for the value of the expression $\sqrt[5]{\frac{32}{243}}$.
Fifth Root Calculation Steps
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Apply Root Property: The fifth root of a fraction can be written as the fraction of the fifth roots:
$ \sqrt[5]{\frac{32}{243}} = \frac{\sqrt[5]{32}}{\sqrt[5]{243}} $
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Evaluate Numerator: Find the number that, when multiplied by itself five times, equals 32. This is $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$. So, $\sqrt[5]{32} = 2$.
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Evaluate Denominator: Find the number that, when multiplied by itself five times, equals 243. This is $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$. So, $\sqrt[5]{243} = 3$.
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Combine Results: Substitute the values back into the fraction:
$ \frac{\sqrt[5]{32}}{\sqrt[5]{243}} = \frac{2}{3} $
Therefore, the value of $\sqrt[5]{\frac{32}{243}}$ is $\frac{2}{3}$.
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Important Questions from Cube and Cube Root
If 5 \(\sqrt{3}\) + \(\sqrt{75}\) = 17.32, then the value of 14 \(\sqrt{3}\) + \(\sqrt{108}\) is:
Find the value of (25)3 + (-29)3 + (4)3
The value of \(\frac{\sqrt[3]{-2744} \times \sqrt[3]{-216}}{\sqrt[3]{\frac{64}{729}}}\) is:
A number is cube of 53. When 7 times of 57 is subtracted from the number, then the resultant number which is formed will be divisible by:
The sum of a positive number and its cube is 1740. What is the value of the number?
