Solve 9h^239h-48=0

Question

Solve the equation

h = \frac{2 3 1014}{39}

Alternative Form

h \approx 0.515203

Evaluate

9 h^{2} \times 39 h - 48 = 0

Multiply

More Steps

Evaluate

9 h^{2} \times 39 h

Multiply the terms

351 h^{2} \times h

Multiply the terms with the same base by adding their exponents

351 h^{2 + 1}

Add the numbers

351 h^{3}

351 h^{3} - 48 = 0

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

351 h^{3} = 0 + 48

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

351 h^{3} = 48

Divide both sides

\frac{351 h ^{3}}{351} = \frac{48}{351}

Divide the numbers

h^{3} = \frac{48}{351}

Cancel out the common factor 3

h^{3} = \frac{16}{117}

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

3 h^{3} = 3 \frac{16}{117}

Calculate

h = 3 \frac{16}{117}

Solution

More Steps

Evaluate

3 \frac{16}{117}

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

\frac{3 16}{3 117}

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{2 3 2}{3 117}

Multiply by the Conjugate

\frac{2 3 2 \times 3 11 7 ^{2}}{3 117 \times 3 11 7 ^{2}}

Simplify

\frac{2 3 2 \times 3 3 507}{3 117 \times 3 11 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

232 \times 33507

Multiply the terms

632 \times 3507

Multiply the terms

631014

\frac{6 3 1014}{3 117 \times 3 11 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

3117 \times 3 11 7^{2}

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

3 117 \times 11 7^{2}

Calculate the product

3 11 7^{3}

Reduce the index of the radical and exponent with 3

117

\frac{6 3 1014}{117}

Cancel out the common factor 3

\frac{2 3 1014}{39}

h = \frac{2 3 1014}{39}

Alternative Form

h \approx 0.515203

Show Solution