Solve 2y^2 5y-462

Question

Simplify the expression

10 y^{3} - 462

Evaluate

2 y^{2} \times 5 y - 462

Solution

More Steps

Evaluate

2 y^{2} \times 5 y

Multiply the terms

10 y^{2} \times y

Multiply the terms with the same base by adding their exponents

10 y^{2 + 1}

Add the numbers

10 y^{3}

10 y^{3} - 462

Show Solution

Factor the expression

2 (5 y^{3} - 231)

Evaluate

2 y^{2} \times 5 y - 462

Multiply

More Steps

Evaluate

2 y^{2} \times 5 y

Multiply the terms

10 y^{2} \times y

Multiply the terms with the same base by adding their exponents

10 y^{2 + 1}

Add the numbers

10 y^{3}

10 y^{3} - 462

Solution

2 (5 y^{3} - 231)

Show Solution

Find the roots

y = \frac{3 5775}{5}

Alternative Form

y \approx 3.588233

Evaluate

2 y^{2} \times 5 y - 462

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

2 y^{2} \times 5 y - 462 = 0

Multiply

More Steps

Multiply the terms

2 y^{2} \times 5 y

Multiply the terms

10 y^{2} \times y

Multiply the terms with the same base by adding their exponents

10 y^{2 + 1}

Add the numbers

10 y^{3}

10 y^{3} - 462 = 0

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

10 y^{3} = 0 + 462

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

10 y^{3} = 462

Divide both sides

\frac{10 y ^{3}}{10} = \frac{462}{10}

Divide the numbers

y^{3} = \frac{462}{10}

Cancel out the common factor 2

y^{3} = \frac{231}{5}

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

3 y^{3} = 3 \frac{231}{5}

Calculate

y = 3 \frac{231}{5}

Solution

More Steps

Evaluate

3 \frac{231}{5}

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

\frac{3 231}{3 5}

Multiply by the Conjugate

\frac{3 231 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 231 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

3231 \times 325

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

3 231 \times 25

Calculate the product

35775

\frac{3 5775}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 5775}{5}

y = \frac{3 5775}{5}

Alternative Form

y \approx 3.588233

Show Solution