Solve 64-81y^4 - ScanMath

Question

Factor the expression

(8 - 9 y^{2}) (8 + 9 y^{2})

Evaluate

64 - 81 y^{4}

Rewrite the expression in exponential form

8^{2} - (9 y^{2})^{2}

Solution

(8 - 9 y^{2}) (8 + 9 y^{2})

Show Solution

y_{1} = - \frac{2 2}{3}, y_{2} = \frac{2 2}{3}

Alternative Form

y_{1} \approx - 0.942809, y_{2} \approx 0.942809

Evaluate

64 - 81 y^{4}

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

64 - 81 y^{4} = 0

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

- 81 y^{4} = 0 - 64

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

- 81 y^{4} = - 64

Change the signs on both sides of the equation

81 y^{4} = 64

Divide both sides

\frac{81 y ^{4}}{81} = \frac{64}{81}

Divide the numbers

y^{4} = \frac{64}{81}

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

y = \pm 4 \frac{64}{81}

Simplify the expression

More Steps

Evaluate

4 \frac{64}{81}

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

\frac{4 64}{4 81}

Simplify the radical expression

More Steps

Evaluate

464

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

4 16 \times 4

Write the number in exponential form with the base of 2

4 2^{4} \times 4

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

4 2^{4} \times 44

Reduce the index of the radical and exponent with 4

244

Simplify the root

22

\frac{2 2}{4 81}

Simplify the radical expression

More Steps

Evaluate

481

Write the number in exponential form with the base of 3

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{2 2}{3}

y = \pm \frac{2 2}{3}

Separate the equation into 2 possible cases

y = \frac{2 2}{3} y = - \frac{2 2}{3}

Solution

y_{1} = - \frac{2 2}{3}, y_{2} = \frac{2 2}{3}

Alternative Form

y_{1} \approx - 0.942809, y_{2} \approx 0.942809

Show Solution