Solve c^6628-25 - ScanMath

Question

Simplify the expression

628 c^{6} - 25

Evaluate

c^{6} \times 628 - 25

Solution

628 c^{6} - 25

Show Solution

c_{1} = - \frac{6 25 \times 62 8 ^{5}}{628}, c_{2} = \frac{6 25 \times 62 8 ^{5}}{628}

Alternative Form

c_{1} \approx - 0.584337, c_{2} \approx 0.584337

Evaluate

c^{6} \times 628 - 25

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

c^{6} \times 628 - 25 = 0

Use the commutative property to reorder the terms

628 c^{6} - 25 = 0

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

628 c^{6} = 0 + 25

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

628 c^{6} = 25

Divide both sides

\frac{628 c ^{6}}{628} = \frac{25}{628}

Divide the numbers

c^{6} = \frac{25}{628}

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

c = \pm 6 \frac{25}{628}

Simplify the expression

More Steps

Evaluate

6 \frac{25}{628}

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

\frac{6 25}{6 628}

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}{6 628}

Multiply by the Conjugate

\frac{3 5 \times 6 62 8 ^{5}}{6 628 \times 6 62 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

35 \times 6 62 8^{5}

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

6 5^{2} \times 6 62 8^{5}

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

6 5^{2} \times 62 8^{5}

Calculate the product

6 25 \times 62 8^{5}

\frac{6 25 \times 62 8 ^{5}}{6 628 \times 6 62 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

6628 \times 6 62 8^{5}

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

6 628 \times 62 8^{5}

Calculate the product

6 62 8^{6}

Reduce the index of the radical and exponent with 6

628

\frac{6 25 \times 62 8 ^{5}}{628}

c = \pm \frac{6 25 \times 62 8 ^{5}}{628}

Separate the equation into 2 possible cases

c = \frac{6 25 \times 62 8 ^{5}}{628} c = - \frac{6 25 \times 62 8 ^{5}}{628}

Solution

c_{1} = - \frac{6 25 \times 62 8 ^{5}}{628}, c_{2} = \frac{6 25 \times 62 8 ^{5}}{628}

Alternative Form

c_{1} \approx - 0.584337, c_{2} \approx 0.584337

Show Solution