Solve b^628-25 - ScanMath

Question

Simplify the expression

28 b^{6} - 25

Evaluate

b^{6} \times 28 - 25

Solution

28 b^{6} - 25

Show Solution

b_{1} = - \frac{6 25 \times 2 8 ^{5}}{28}, b_{2} = \frac{6 25 \times 2 8 ^{5}}{28}

Alternative Form

b_{1} \approx - 0.981289, b_{2} \approx 0.981289

Evaluate

b^{6} \times 28 - 25

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

b^{6} \times 28 - 25 = 0

Use the commutative property to reorder the terms

28 b^{6} - 25 = 0

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

28 b^{6} = 0 + 25

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

28 b^{6} = 25

Divide both sides

\frac{28 b ^{6}}{28} = \frac{25}{28}

Divide the numbers

b^{6} = \frac{25}{28}

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

b = \pm 6 \frac{25}{28}

Simplify the expression

More Steps

Evaluate

6 \frac{25}{28}

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

\frac{6 25}{6 28}

Simplify the radical expression

More Steps

Evaluate

625

Write the number in exponential form with the base of 5

6 5^{2}

Reduce the index of the radical and exponent with 2

35

\frac{3 5}{6 28}

Multiply by the Conjugate

\frac{3 5 \times 6 2 8 ^{5}}{6 28 \times 6 2 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

35 \times 6 2 8^{5}

Use n a = mn a^{m} to expand the expression

6 5^{2} \times 6 2 8^{5}

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

6 5^{2} \times 2 8^{5}

Calculate the product

6 25 \times 2 8^{5}

\frac{6 25 \times 2 8 ^{5}}{6 28 \times 6 2 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

628 \times 6 2 8^{5}

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

6 28 \times 2 8^{5}

Calculate the product

6 2 8^{6}

Reduce the index of the radical and exponent with 6

28

\frac{6 25 \times 2 8 ^{5}}{28}

b = \pm \frac{6 25 \times 2 8 ^{5}}{28}

Separate the equation into 2 possible cases

b = \frac{6 25 \times 2 8 ^{5}}{28} b = - \frac{6 25 \times 2 8 ^{5}}{28}

Solution

b_{1} = - \frac{6 25 \times 2 8 ^{5}}{28}, b_{2} = \frac{6 25 \times 2 8 ^{5}}{28}

Alternative Form

b_{1} \approx - 0.981289, b_{2} \approx 0.981289

Show Solution