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Question
x^{2}\times 10x=24
Solve the equation
x=\frac{\sqrt[3]{300}}{5}
Alternative Form
x\approx 1.338866
Evaluate
x^{2}\times 10x=24
Multiply
More Steps
Evaluate
x^{2}\times 10x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 10
Add the numbers
x^{3}\times 10
Use the commutative property to reorder the terms
10x^{3}
10x^{3}=24
Divide both sides
\frac{10x^{3}}{10}=\frac{24}{10}
Divide the numbers
x^{3}=\frac{24}{10}
\text{Cancel out the common factor }2
x^{3}=\frac{12}{5}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{\frac{12}{5}}
Calculate
x=\sqrt[3]{\frac{12}{5}}
Solution
More Steps
Evaluate
\sqrt[3]{\frac{12}{5}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{12}}{\sqrt[3]{5}}
Multiply by the Conjugate
\frac{\sqrt[3]{12}\times \sqrt[3]{5^{2}}}{\sqrt[3]{5}\times \sqrt[3]{5^{2}}}
Simplify
\frac{\sqrt[3]{12}\times \sqrt[3]{25}}{\sqrt[3]{5}\times \sqrt[3]{5^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{12}\times \sqrt[3]{25}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{12\times 25}
Calculate the product
\sqrt[3]{300}
\frac{\sqrt[3]{300}}{\sqrt[3]{5}\times \sqrt[3]{5^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{5}\times \sqrt[3]{5^{2}}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{5\times 5^{2}}
Calculate the product
\sqrt[3]{5^{3}}
\text{Reduce the index of the radical and exponent with }3
5
\frac{\sqrt[3]{300}}{5}
x=\frac{\sqrt[3]{300}}{5}
Alternative Form
x\approx 1.338866
Show Solutions
Graph
