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Question
h^{3}\times 136-6\frac{7}{16}
Simplify the expression
136h^{3}-\frac{103}{16}
Evaluate
h^{3}\times 136-6\frac{7}{16}
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
6\frac{7}{16}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{6\times 16+7}{16}
Multiply the terms
\frac{96+7}{16}
Add the terms
\frac{103}{16}
h^{3}\times 136-\frac{103}{16}
Solution
136h^{3}-\frac{103}{16}
Show Solutions
Factor the expression
\frac{1}{16}\left(2176h^{3}-103\right)
Evaluate
h^{3}\times 136-6\frac{7}{16}
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
6\frac{7}{16}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{6\times 16+7}{16}
Multiply the terms
\frac{96+7}{16}
Add the terms
\frac{103}{16}
h^{3}\times 136-\frac{103}{16}
Use the commutative property to reorder the terms
136h^{3}-\frac{103}{16}
Solution
\frac{1}{16}\left(2176h^{3}-103\right)
Show Solutions
Find the roots
h=\frac{\sqrt[3]{119068}}{136}
Alternative Form
h\approx 0.361737
Evaluate
h^{3}\times 136-6\frac{7}{16}
To find the roots of the expression,set the expression equal to 0
h^{3}\times 136-6\frac{7}{16}=0
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
6\frac{7}{16}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{6\times 16+7}{16}
Multiply the terms
\frac{96+7}{16}
Add the terms
\frac{103}{16}
h^{3}\times 136-\frac{103}{16}=0
Use the commutative property to reorder the terms
136h^{3}-\frac{103}{16}=0
Move the constant to the right-hand side and change its sign
136h^{3}=0+\frac{103}{16}
Add the terms
136h^{3}=\frac{103}{16}
Multiply by the reciprocal
136h^{3}\times \frac{1}{136}=\frac{103}{16}\times \frac{1}{136}
Multiply
h^{3}=\frac{103}{16}\times \frac{1}{136}
Multiply
More Steps
Evaluate
\frac{103}{16}\times \frac{1}{136}
To multiply the fractions,multiply the numerators and denominators separately
\frac{103}{16\times 136}
Multiply the numbers
\frac{103}{2176}
h^{3}=\frac{103}{2176}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{h^{3}}=\sqrt[3]{\frac{103}{2176}}
Calculate
h=\sqrt[3]{\frac{103}{2176}}
Solution
More Steps
Evaluate
\sqrt[3]{\frac{103}{2176}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{103}}{\sqrt[3]{2176}}
Simplify the radical expression
More Steps
Evaluate
\sqrt[3]{2176}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt[3]{64\times 34}
\text{Write the number in exponential form with the base of }4
\sqrt[3]{4^{3}\times 34}
The root of a product is equal to the product of the roots of each factor
\sqrt[3]{4^{3}}\times \sqrt[3]{34}
\text{Reduce the index of the radical and exponent with }3
4\sqrt[3]{34}
\frac{\sqrt[3]{103}}{4\sqrt[3]{34}}
Multiply by the Conjugate
\frac{\sqrt[3]{103}\times \sqrt[3]{34^{2}}}{4\sqrt[3]{34}\times \sqrt[3]{34^{2}}}
Simplify
\frac{\sqrt[3]{103}\times \sqrt[3]{1156}}{4\sqrt[3]{34}\times \sqrt[3]{34^{2}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[3]{103}\times \sqrt[3]{1156}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{103\times 1156}
Calculate the product
\sqrt[3]{119068}
\frac{\sqrt[3]{119068}}{4\sqrt[3]{34}\times \sqrt[3]{34^{2}}}
Multiply the numbers
More Steps
Evaluate
4\sqrt[3]{34}\times \sqrt[3]{34^{2}}
Multiply the terms
4\times 34
Multiply the terms
136
\frac{\sqrt[3]{119068}}{136}
h=\frac{\sqrt[3]{119068}}{136}
Alternative Form
h\approx 0.361737
Show Solutions
