Solve 9c^6001-33 - Socratic AI (ScanMath)

Question

Simplify the expression

9 c^{6} - 33

Evaluate

9 c^{6} \times 1 - 33

Solution

9 c^{6} - 33

Show Solution

3 (3 c^{6} - 11)

Evaluate

9 c^{6} \times 1 - 33

Multiply the terms

9 c^{6} - 33

Solution

3 (3 c^{6} - 11)

Show Solution

c_{1} = - \frac{6 2673}{3}, c_{2} = \frac{6 2673}{3}

Alternative Form

c_{1} \approx - 1.241782, c_{2} \approx 1.241782

Evaluate

9 c^{6} \times 1 - 33

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

9 c^{6} \times 1 - 33 = 0

Multiply the terms

9 c^{6} - 33 = 0

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

9 c^{6} = 0 + 33

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

9 c^{6} = 33

Divide both sides

\frac{9 c ^{6}}{9} = \frac{33}{9}

Divide the numbers

c^{6} = \frac{33}{9}

Cancel out the common factor 3

c^{6} = \frac{11}{3}

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

c = \pm 6 \frac{11}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{11}{3}

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

\frac{6 11}{6 3}

Multiply by the Conjugate

\frac{6 11 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 11 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

611 \times 6243

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

6 11 \times 243

Calculate the product

62673

\frac{6 2673}{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 2673}{3}

c = \pm \frac{6 2673}{3}

Separate the equation into 2 possible cases

c = \frac{6 2673}{3} c = - \frac{6 2673}{3}

Solution

c_{1} = - \frac{6 2673}{3}, c_{2} = \frac{6 2673}{3}

Alternative Form

c_{1} \approx - 1.241782, c_{2} \approx 1.241782

Show Solution