Solve 1b^6003-1 - Socratic AI (ScanMath)

Question

Simplify the expression

3 b^{6} - 1

Evaluate

1 \times b^{6} \times 3 - 1

Solution

More Steps

Evaluate

1 \times b^{6} \times 3

Rewrite the expression

b^{6} \times 3

Use the commutative property to reorder the terms

3 b^{6}

3 b^{6} - 1

Show Solution

b_{1} = - \frac{6 243}{3}, b_{2} = \frac{6 243}{3}

Alternative Form

b_{1} \approx - 0.832683, b_{2} \approx 0.832683

Evaluate

1 \times b^{6} \times 3 - 1

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

1 \times b^{6} \times 3 - 1 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times b^{6} \times 3

Rewrite the expression

b^{6} \times 3

Use the commutative property to reorder the terms

3 b^{6}

3 b^{6} - 1 = 0

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

3 b^{6} = 0 + 1

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

3 b^{6} = 1

Divide both sides

\frac{3 b ^{6}}{3} = \frac{1}{3}

Divide the numbers

b^{6} = \frac{1}{3}

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

b = \pm 6 \frac{1}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{3}

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

\frac{6 1}{6 3}

Simplify the radical expression

\frac{1}{6 3}

Multiply by the Conjugate

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

Simplify

\frac{6 243}{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{6 243}{3}

b = \pm \frac{6 243}{3}

Separate the equation into 2 possible cases

b = \frac{6 243}{3} b = - \frac{6 243}{3}

Solution

b_{1} = - \frac{6 243}{3}, b_{2} = \frac{6 243}{3}

Alternative Form

b_{1} \approx - 0.832683, b_{2} \approx 0.832683

Show Solution