Solve 8t^240t-33 - ScanMath

Question

Simplify the expression

320 t^{3} - 33

Evaluate

8 t^{2} \times 40 t - 33

Solution

More Steps

Evaluate

8 t^{2} \times 40 t

Multiply the terms

320 t^{2} \times t

Multiply the terms with the same base by adding their exponents

320 t^{2 + 1}

Add the numbers

320 t^{3}

320 t^{3} - 33

Show Solution

t = \frac{3 825}{20}

Alternative Form

t \approx 0.468944

Evaluate

8 t^{2} \times 40 t - 33

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

8 t^{2} \times 40 t - 33 = 0

Multiply

More Steps

Multiply the terms

8 t^{2} \times 40 t

Multiply the terms

320 t^{2} \times t

Multiply the terms with the same base by adding their exponents

320 t^{2 + 1}

Add the numbers

320 t^{3}

320 t^{3} - 33 = 0

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

320 t^{3} = 0 + 33

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

320 t^{3} = 33

Divide both sides

\frac{320 t ^{3}}{320} = \frac{33}{320}

Divide the numbers

t^{3} = \frac{33}{320}

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

3 t^{3} = 3 \frac{33}{320}

Calculate

t = 3 \frac{33}{320}

Solution

More Steps

Evaluate

3 \frac{33}{320}

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

\frac{3 33}{3 320}

Simplify the radical expression

More Steps

Evaluate

3320

Write the expression as a product where the root of one of the factors can be evaluated

3 64 \times 5

Write the number in exponential form with the base of 4

3 4^{3} \times 5

The root of a product is equal to the product of the roots of each factor

3 4^{3} \times 35

Reduce the index of the radical and exponent with 3

435

\frac{3 33}{4 3 5}

Multiply by the Conjugate

\frac{3 33 \times 3 5 ^{2}}{4 3 5 \times 3 5 ^{2}}

Simplify

\frac{3 33 \times 3 25}{4 3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

333 \times 325

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

3 33 \times 25

Calculate the product

3825

\frac{3 825}{4 3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

435 \times 3 5^{2}

Multiply the terms

4 \times 5

Multiply the terms

20

\frac{3 825}{20}

t = \frac{3 825}{20}

Alternative Form

t \approx 0.468944

Show Solution