Solve 13y^2 6y -99

Question

Simplify the expression

78 y^{3} - 99

Evaluate

13 y^{2} \times 6 y - 99

Solution

More Steps

Evaluate

13 y^{2} \times 6 y

Multiply the terms

78 y^{2} \times y

Multiply the terms with the same base by adding their exponents

78 y^{2 + 1}

Add the numbers

78 y^{3}

78 y^{3} - 99

Show Solution

Factor the expression

3 (26 y^{3} - 33)

Evaluate

13 y^{2} \times 6 y - 99

Multiply

More Steps

Evaluate

13 y^{2} \times 6 y

Multiply the terms

78 y^{2} \times y

Multiply the terms with the same base by adding their exponents

78 y^{2 + 1}

Add the numbers

78 y^{3}

78 y^{3} - 99

Solution

3 (26 y^{3} - 33)

Show Solution

Find the roots

y = \frac{3 22308}{26}

Alternative Form

y \approx 1.082713

Evaluate

13 y^{2} \times 6 y - 99

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

13 y^{2} \times 6 y - 99 = 0

Multiply

More Steps

Multiply the terms

13 y^{2} \times 6 y

Multiply the terms

78 y^{2} \times y

Multiply the terms with the same base by adding their exponents

78 y^{2 + 1}

Add the numbers

78 y^{3}

78 y^{3} - 99 = 0

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

78 y^{3} = 0 + 99

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

78 y^{3} = 99

Divide both sides

\frac{78 y ^{3}}{78} = \frac{99}{78}

Divide the numbers

y^{3} = \frac{99}{78}

Cancel out the common factor 3

y^{3} = \frac{33}{26}

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

3 y^{3} = 3 \frac{33}{26}

Calculate

y = 3 \frac{33}{26}

Solution

More Steps

Evaluate

3 \frac{33}{26}

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

\frac{3 33}{3 26}

Multiply by the Conjugate

\frac{3 33 \times 3 2 6 ^{2}}{3 26 \times 3 2 6 ^{2}}

Simplify

\frac{3 33 \times 3 676}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

333 \times 3676

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

3 33 \times 676

Calculate the product

322308

\frac{3 22308}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

326 \times 3 2 6^{2}

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

3 26 \times 2 6^{2}

Calculate the product

3 2 6^{3}

Reduce the index of the radical and exponent with 3

26

\frac{3 22308}{26}

y = \frac{3 22308}{26}

Alternative Form

y \approx 1.082713

Show Solution