Solve 49b^(4)-64 - ScanMath

Question

Factor the expression

(7 b^{2} - 8) (7 b^{2} + 8)

Evaluate

49 b^{4} - 64

Rewrite the expression in exponential form

(7 b^{2})^{2} - 8^{2}

Solution

(7 b^{2} - 8) (7 b^{2} + 8)

Show Solution

b_{1} = - \frac{2 14}{7}, b_{2} = \frac{2 14}{7}

Alternative Form

b_{1} \approx - 1.069045, b_{2} \approx 1.069045

Evaluate

49 b^{4} - 64

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

49 b^{4} - 64 = 0

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

49 b^{4} = 0 + 64

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

49 b^{4} = 64

Divide both sides

\frac{49 b ^{4}}{49} = \frac{64}{49}

Divide the numbers

b^{4} = \frac{64}{49}

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

b = \pm 4 \frac{64}{49}

Simplify the expression

More Steps

Evaluate

4 \frac{64}{49}

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

\frac{4 64}{4 49}

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 49}

Simplify the radical expression

More Steps

Evaluate

449

Write the number in exponential form with the base of 7

4 7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{2 2}{7}

Multiply by the Conjugate

\frac{2 2 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

2 \times 7

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

2 \times 7

Calculate the product

14

\frac{2 14}{7 \times 7}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2 14}{7}

b = \pm \frac{2 14}{7}

Separate the equation into 2 possible cases

b = \frac{2 14}{7} b = - \frac{2 14}{7}

Solution

b_{1} = - \frac{2 14}{7}, b_{2} = \frac{2 14}{7}

Alternative Form

b_{1} \approx - 1.069045, b_{2} \approx 1.069045

Show Solution