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Question
h^{3}\times 138-6\frac{3}{4}
Simplify the expression
138h^{3}-\frac{27}{4}
Evaluate
h^{3}\times 138-6\frac{3}{4}
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
6\frac{3}{4}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{6\times 4+3}{4}
Multiply the terms
\frac{24+3}{4}
Add the terms
\frac{27}{4}
h^{3}\times 138-\frac{27}{4}
Solution
138h^{3}-\frac{27}{4}
Show Solutions
Factor the expression
\frac{3}{4}\left(184h^{3}-9\right)
Evaluate
h^{3}\times 138-6\frac{3}{4}
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
6\frac{3}{4}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{6\times 4+3}{4}
Multiply the terms
\frac{24+3}{4}
Add the terms
\frac{27}{4}
h^{3}\times 138-\frac{27}{4}
Use the commutative property to reorder the terms
138h^{3}-\frac{27}{4}
Solution
\frac{3}{4}\left(184h^{3}-9\right)
Show Solutions
Find the roots
h=\frac{\sqrt[3]{4761}}{46}
Alternative Form
h\approx 0.365714
Evaluate
h^{3}\times 138-6\frac{3}{4}
To find the roots of the expression,set the expression equal to 0
h^{3}\times 138-6\frac{3}{4}=0
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
6\frac{3}{4}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{6\times 4+3}{4}
Multiply the terms
\frac{24+3}{4}
Add the terms
\frac{27}{4}
h^{3}\times 138-\frac{27}{4}=0
Use the commutative property to reorder the terms
138h^{3}-\frac{27}{4}=0
Move the constant to the right-hand side and change its sign
138h^{3}=0+\frac{27}{4}
Add the terms
138h^{3}=\frac{27}{4}
Multiply by the reciprocal
138h^{3}\times \frac{1}{138}=\frac{27}{4}\times \frac{1}{138}
Multiply
h^{3}=\frac{27}{4}\times \frac{1}{138}
Multiply
More Steps
Evaluate
\frac{27}{4}\times \frac{1}{138}
Reduce the numbers
\frac{9}{4}\times \frac{1}{46}
To multiply the fractions,multiply the numerators and denominators separately
\frac{9}{4\times 46}
Multiply the numbers
\frac{9}{184}
h^{3}=\frac{9}{184}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{h^{3}}=\sqrt[3]{\frac{9}{184}}
Calculate
h=\sqrt[3]{\frac{9}{184}}
Solution
More Steps
Evaluate
\sqrt[3]{\frac{9}{184}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{9}}{\sqrt[3]{184}}
Simplify the radical expression
More Steps
Evaluate
\sqrt[3]{184}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt[3]{8\times 23}
\text{Write the number in exponential form with the base of }2
\sqrt[3]{2^{3}\times 23}
The root of a product is equal to the product of the roots of each factor
\sqrt[3]{2^{3}}\times \sqrt[3]{23}
\text{Reduce the index of the radical and exponent with }3
2\sqrt[3]{23}
\frac{\sqrt[3]{9}}{2\sqrt[3]{23}}
Multiply by the Conjugate
\frac{\sqrt[3]{9}\times \sqrt[3]{23^{2}}}{2\sqrt[3]{23}\times \sqrt[3]{23^{2}}}
Simplify
\frac{\sqrt[3]{9}\times \sqrt[3]{529}}{2\sqrt[3]{23}\times \sqrt[3]{23^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{9}\times \sqrt[3]{529}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{9\times 529}
Calculate the product
\sqrt[3]{4761}
\frac{\sqrt[3]{4761}}{2\sqrt[3]{23}\times \sqrt[3]{23^{2}}}
Multiply the numbers
More Steps
Evaluate
2\sqrt[3]{23}\times \sqrt[3]{23^{2}}
Multiply the terms
2\times 23
Multiply the terms
46
\frac{\sqrt[3]{4761}}{46}
h=\frac{\sqrt[3]{4761}}{46}
Alternative Form
h\approx 0.365714
Show Solutions
