Solve 3x^37=16 - ScanMath

Question

Solve the equation

x = \frac{2 3 882}{21}

Alternative Form

x \approx 0.913342

Evaluate

3 x^{3} \times 7 = 16

Multiply the terms

21 x^{3} = 16

Divide both sides

\frac{21 x ^{3}}{21} = \frac{16}{21}

Divide the numbers

x^{3} = \frac{16}{21}

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

3 x^{3} = 3 \frac{16}{21}

Calculate

x = 3 \frac{16}{21}

Solution

More Steps

Evaluate

3 \frac{16}{21}

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

\frac{3 16}{3 21}

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 21}

Multiply by the Conjugate

\frac{2 3 2 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{2 3 2 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3441

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

3 2 \times 441

Calculate the product

3882

\frac{2 3 882}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3 2 1^{2}

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

3 21 \times 2 1^{2}

Calculate the product

3 2 1^{3}

Reduce the index of the radical and exponent with 3

21

\frac{2 3 882}{21}

x = \frac{2 3 882}{21}

Alternative Form

x \approx 0.913342

Show Solution