Solve 146 = (5y^3) (4y 8)

Question

Solve the equation

y_{1} = - \frac{4 9125}{10}, y_{2} = \frac{4 9125}{10}

Alternative Form

y_{1} \approx - 0.977368, y_{2} \approx 0.977368

Evaluate

146 = 5 y^{3} (4 y \times 8)

Remove the parentheses

146 = 5 y^{3} \times 4 y \times 8

Multiply

More Steps

Evaluate

5 y^{3} \times 4 y \times 8

Multiply the terms

More Steps

Evaluate

5 \times 4 \times 8

Multiply the terms

20 \times 8

Multiply the numbers

160

160 y^{3} \times y

Multiply the terms with the same base by adding their exponents

160 y^{3 + 1}

Add the numbers

160 y^{4}

146 = 160 y^{4}

Swap the sides of the equation

160 y^{4} = 146

Divide both sides

\frac{160 y ^{4}}{160} = \frac{146}{160}

Divide the numbers

y^{4} = \frac{146}{160}

Cancel out the common factor 2

y^{4} = \frac{73}{80}

Take the root of both sides of the equation and remember to use both positive and negative roots

y = \pm 4 \frac{73}{80}

Simplify the expression

More Steps

Evaluate

4 \frac{73}{80}

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

\frac{4 73}{4 80}

Simplify the radical expression

More Steps

Evaluate

480

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

4 16 \times 5

Write the number in exponential form with the base of 2

4 2^{4} \times 5

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

4 2^{4} \times 45

Reduce the index of the radical and exponent with 4

245

\frac{4 73}{2 4 5}

Multiply by the Conjugate

\frac{4 73 \times 4 5 ^{3}}{2 4 5 \times 4 5 ^{3}}

Simplify

\frac{4 73 \times 4 125}{2 4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

473 \times 4125

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

4 73 \times 125

Calculate the product

49125

\frac{4 9125}{2 4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

245 \times 4 5^{3}

Multiply the terms

2 \times 5

Multiply the terms

10

\frac{4 9125}{10}

y = \pm \frac{4 9125}{10}

Separate the equation into 2 possible cases

y = \frac{4 9125}{10} y = - \frac{4 9125}{10}

Solution

y_{1} = - \frac{4 9125}{10}, y_{2} = \frac{4 9125}{10}

Alternative Form

y_{1} \approx - 0.977368, y_{2} \approx 0.977368

Show Solution