Solve r^689/2024-2 - Socratic AI (ScanMath)

Question

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 Solution

\frac{1}{2024} (89 r^{6} - 4048)

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} (89 r^{6} - 4048)

Show Solution

r_{1} = - \frac{6 4048 \times 8 9 ^{5}}{89}, r_{2} = \frac{6 4048 \times 8 9 ^{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 6 \frac{4048}{89}

Simplify the expression

More Steps

Evaluate

6 \frac{4048}{89}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 4048}{6 89}

Multiply by the Conjugate

\frac{6 4048 \times 6 8 9 ^{5}}{6 89 \times 6 8 9 ^{5}}

The product of roots with the same index is equal to the root of the product

\frac{6 4048 \times 8 9 ^{5}}{6 89 \times 6 8 9 ^{5}}

Multiply the numbers

More Steps

Evaluate

689 \times 6 8 9^{5}

The product of roots with the same index is equal to the root of the product

6 89 \times 8 9^{5}

Calculate the product

6 8 9^{6}

Reduce the index of the radical and exponent with 6

89

\frac{6 4048 \times 8 9 ^{5}}{89}

r = \pm \frac{6 4048 \times 8 9 ^{5}}{89}

Separate the equation into 2 possible cases

r = \frac{6 4048 \times 8 9 ^{5}}{89} r = - \frac{6 4048 \times 8 9 ^{5}}{89}

Solution

r_{1} = - \frac{6 4048 \times 8 9 ^{5}}{89}, r_{2} = \frac{6 4048 \times 8 9 ^{5}}{89}

Alternative Form

r_{1} \approx - 1.889333, r_{2} \approx 1.889333

Show Solution