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Question
r^{6}\times \frac{89}{2024}-2
Simplify the expression
\frac{89}{2024}r^{6}-2
Evaluate
r^{6}\times \frac{89}{2024}-2
Solution
\frac{89}{2024}r^{6}-2
Show Solutions
Factor the expression
\frac{1}{2024}\left(89r^{6}-4048\right)
Evaluate
r^{6}\times \frac{89}{2024}-2
Use the commutative property to reorder the terms
\frac{89}{2024}r^{6}-2
Solution
\frac{1}{2024}\left(89r^{6}-4048\right)
Show Solutions
Find the roots
r_{1}=-\frac{\sqrt[6]{4048\times 89^{5}}}{89},r_{2}=\frac{\sqrt[6]{4048\times 89^{5}}}{89}
Alternative Form
r_{1}\approx -1.889333,r_{2}\approx 1.889333
Evaluate
r^{6}\times \frac{89}{2024}-2
To find the roots of the expression,set the expression equal to 0
r^{6}\times \frac{89}{2024}-2=0
Use the commutative property to reorder the terms
\frac{89}{2024}r^{6}-2=0
Move the constant to the right-hand side and change its sign
\frac{89}{2024}r^{6}=0+2
Removing 0 doesn't change the value,so remove it from the expression
\frac{89}{2024}r^{6}=2
Multiply by the reciprocal
\frac{89}{2024}r^{6}\times \frac{2024}{89}=2\times \frac{2024}{89}
Multiply
r^{6}=2\times \frac{2024}{89}
Multiply
More Steps
Evaluate
2\times \frac{2024}{89}
Multiply the numbers
\frac{2\times 2024}{89}
Multiply the numbers
\frac{4048}{89}
r^{6}=\frac{4048}{89}
Take the root of both sides of the equation and remember to use both positive and negative roots
r=\pm \sqrt[6]{\frac{4048}{89}}
Simplify the expression
More Steps
Evaluate
\sqrt[6]{\frac{4048}{89}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[6]{4048}}{\sqrt[6]{89}}
Multiply by the Conjugate
\frac{\sqrt[6]{4048}\times \sqrt[6]{89^{5}}}{\sqrt[6]{89}\times \sqrt[6]{89^{5}}}
The product of roots with the same index is equal to the root of the product
\frac{\sqrt[6]{4048\times 89^{5}}}{\sqrt[6]{89}\times \sqrt[6]{89^{5}}}
Multiply the numbers
More Steps
Evaluate
\sqrt[6]{89}\times \sqrt[6]{89^{5}}
The product of roots with the same index is equal to the root of the product
\sqrt[6]{89\times 89^{5}}
Calculate the product
\sqrt[6]{89^{6}}
\text{Reduce the index of the radical and exponent with }6
89
\frac{\sqrt[6]{4048\times 89^{5}}}{89}
r=\pm \frac{\sqrt[6]{4048\times 89^{5}}}{89}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&r=\frac{\sqrt[6]{4048\times 89^{5}}}{89}\\&r=-\frac{\sqrt[6]{4048\times 89^{5}}}{89}\end{align}
Solution
r_{1}=-\frac{\sqrt[6]{4048\times 89^{5}}}{89},r_{2}=\frac{\sqrt[6]{4048\times 89^{5}}}{89}
Alternative Form
r_{1}\approx -1.889333,r_{2}\approx 1.889333
Show Solutions
