Solve t^34-110-0 - Socratic AI (ScanMath)

Question

Simplify the expression

4 t^{3} - 110

Evaluate

t^{3} \times 4 - 110 - 0

Use the commutative property to reorder the terms

4 t^{3} - 110 - 0

Solution

4 t^{3} - 110

Show Solution

2 (2 t^{3} - 55)

Evaluate

t^{3} \times 4 - 110 - 0

Use the commutative property to reorder the terms

4 t^{3} - 110 - 0

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

4 t^{3} - 110

Solution

2 (2 t^{3} - 55)

Show Solution

t = \frac{3 220}{2}

Alternative Form

t \approx 3.018405

Evaluate

t^{3} \times 4 - 110 - 0

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

t^{3} \times 4 - 110 - 0 = 0

Use the commutative property to reorder the terms

4 t^{3} - 110 - 0 = 0

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

4 t^{3} - 110 = 0

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

4 t^{3} = 0 + 110

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

4 t^{3} = 110

Divide both sides

\frac{4 t ^{3}}{4} = \frac{110}{4}

Divide the numbers

t^{3} = \frac{110}{4}

Cancel out the common factor 2

t^{3} = \frac{55}{2}

Take the 3 -th root on both sides of the equation

3 t^{3} = 3 \frac{55}{2}

Calculate

t = 3 \frac{55}{2}

Solution

More Steps

Evaluate

3 \frac{55}{2}

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

\frac{3 55}{3 2}

Multiply by the Conjugate

\frac{3 55 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 55 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

355 \times 34

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

3 55 \times 4

Calculate the product

3220

\frac{3 220}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 220}{2}

t = \frac{3 220}{2}

Alternative Form

t \approx 3.018405

Show Solution