Solve y^27y-8=0 - ScanMath

Question

Solve the equation

y = \frac{2 3 49}{7}

Alternative Form

y \approx 1.045516

Evaluate

y^{2} \times 7 y - 8 = 0

Multiply

More Steps

Evaluate

y^{2} \times 7 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 7

Add the numbers

y^{3} \times 7

Use the commutative property to reorder the terms

7 y^{3}

7 y^{3} - 8 = 0

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

7 y^{3} = 0 + 8

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

7 y^{3} = 8

Divide both sides

\frac{7 y ^{3}}{7} = \frac{8}{7}

Divide the numbers

y^{3} = \frac{8}{7}

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

3 y^{3} = 3 \frac{8}{7}

Calculate

y = 3 \frac{8}{7}

Solution

More Steps

Evaluate

3 \frac{8}{7}

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

\frac{3 8}{3 7}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{3 7}

Multiply by the Conjugate

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

Simplify

\frac{2 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{2 3 49}{7}

y = \frac{2 3 49}{7}

Alternative Form

y \approx 1.045516

Show Solution