Solve t^248t-324 - ScanMath

Question

Simplify the expression

48 t^{3} - 324

Evaluate

t^{2} \times 48 t - 324

Solution

More Steps

Evaluate

t^{2} \times 48 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 48

Add the numbers

t^{3} \times 48

Use the commutative property to reorder the terms

48 t^{3}

48 t^{3} - 324

Show Solution

Factor the expression

12 (4 t^{3} - 27)

Evaluate

t^{2} \times 48 t - 324

Multiply

More Steps

Evaluate

t^{2} \times 48 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 48

Add the numbers

t^{3} \times 48

Use the commutative property to reorder the terms

48 t^{3}

48 t^{3} - 324

Solution

12 (4 t^{3} - 27)

Show Solution

Find the roots

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

Alternative Form

t \approx 1.889882

Evaluate

t^{2} \times 48 t - 324

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

t^{2} \times 48 t - 324 = 0

Multiply

More Steps

Multiply the terms

t^{2} \times 48 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 48

Add the numbers

t^{3} \times 48

Use the commutative property to reorder the terms

48 t^{3}

48 t^{3} - 324 = 0

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

48 t^{3} = 0 + 324

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

48 t^{3} = 324

Divide both sides

\frac{48 t ^{3}}{48} = \frac{324}{48}

Divide the numbers

t^{3} = \frac{324}{48}

Cancel out the common factor 12

t^{3} = \frac{27}{4}

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

3 t^{3} = 3 \frac{27}{4}

Calculate

t = 3 \frac{27}{4}

Solution

More Steps

Evaluate

3 \frac{27}{4}

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

\frac{3 27}{3 4}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3}{3 4}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{6 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{6 3 2}{2 ^{2}}

Rewrite the expression

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

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 3 2}{2}

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

Alternative Form

t \approx 1.889882

Show Solution