Solve 6g^248g-54 - ScanMath

Question

Simplify the expression

288 g^{3} - 54

Evaluate

6 g^{2} \times 48 g - 54

Solution

More Steps

Evaluate

6 g^{2} \times 48 g

Multiply the terms

288 g^{2} \times g

Multiply the terms with the same base by adding their exponents

288 g^{2 + 1}

Add the numbers

288 g^{3}

288 g^{3} - 54

Show Solution

Factor the expression

18 (16 g^{3} - 3)

Evaluate

6 g^{2} \times 48 g - 54

Multiply

More Steps

Evaluate

6 g^{2} \times 48 g

Multiply the terms

288 g^{2} \times g

Multiply the terms with the same base by adding their exponents

288 g^{2 + 1}

Add the numbers

288 g^{3}

288 g^{3} - 54

Solution

18 (16 g^{3} - 3)

Show Solution

Find the roots

g = \frac{3 12}{4}

Alternative Form

g \approx 0.572357

Evaluate

6 g^{2} \times 48 g - 54

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

6 g^{2} \times 48 g - 54 = 0

Multiply

More Steps

Multiply the terms

6 g^{2} \times 48 g

Multiply the terms

288 g^{2} \times g

Multiply the terms with the same base by adding their exponents

288 g^{2 + 1}

Add the numbers

288 g^{3}

288 g^{3} - 54 = 0

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

288 g^{3} = 0 + 54

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

288 g^{3} = 54

Divide both sides

\frac{288 g ^{3}}{288} = \frac{54}{288}

Divide the numbers

g^{3} = \frac{54}{288}

Cancel out the common factor 18

g^{3} = \frac{3}{16}

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

3 g^{3} = 3 \frac{3}{16}

Calculate

g = 3 \frac{3}{16}

Solution

More Steps

Evaluate

3 \frac{3}{16}

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

\frac{3 3}{3 16}

Simplify the radical expression

More Steps

Evaluate

316

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

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

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

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{3 3}{2 3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

\frac{3 12}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

232 \times 3 2^{2}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{3 12}{4}

g = \frac{3 12}{4}

Alternative Form

g \approx 0.572357

Show Solution