Solve r^63-192-280

Question

Simplify the expression

3 r^{6} - 472

Evaluate

r^{6} \times 3 - 192 - 280

Use the commutative property to reorder the terms

3 r^{6} - 192 - 280

Solution

3 r^{6} - 472

Show Solution

r_{1} = - \frac{6 114696}{3}, r_{2} = \frac{6 114696}{3}

Alternative Form

r_{1} \approx - 2.323469, r_{2} \approx 2.323469

Evaluate

r^{6} \times 3 - 192 - 280

To find the roots of the expression,set the expression equal to 0

r^{6} \times 3 - 192 - 280 = 0

Use the commutative property to reorder the terms

3 r^{6} - 192 - 280 = 0

Subtract the numbers

3 r^{6} - 472 = 0

Move the constant to the right-hand side and change its sign

3 r^{6} = 0 + 472

Removing 0 doesn't change the value,so remove it from the expression

3 r^{6} = 472

Divide both sides

\frac{3 r ^{6}}{3} = \frac{472}{3}

Divide the numbers

r^{6} = \frac{472}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

r = \pm 6 \frac{472}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{472}{3}

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

\frac{6 472}{6 3}

Multiply by the Conjugate

\frac{6 472 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 472 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

6472 \times 6243

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

6 472 \times 243

Calculate the product

6114696

\frac{6 114696}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 6 3^{5}

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

6 3 \times 3^{5}

Calculate the product

6 3^{6}

Reduce the index of the radical and exponent with 6

3

\frac{6 114696}{3}

r = \pm \frac{6 114696}{3}

Separate the equation into 2 possible cases

r = \frac{6 114696}{3} r = - \frac{6 114696}{3}

Solution

r_{1} = - \frac{6 114696}{3}, r_{2} = \frac{6 114696}{3}

Alternative Form

r_{1} \approx - 2.323469, r_{2} \approx 2.323469

Show Solution