Solve 1v^4204-157

Question

Simplify the expression

204 v^{4} - 157

Evaluate

1 \times v^{4} \times 204 - 157

Solution

More Steps

Evaluate

1 \times v^{4} \times 204

Rewrite the expression

v^{4} \times 204

Use the commutative property to reorder the terms

204 v^{4}

204 v^{4} - 157

Show Solution

v_{1} = - \frac{4 157 \times 20 4 ^{3}}{204}, v_{2} = \frac{4 157 \times 20 4 ^{3}}{204}

Alternative Form

v_{1} \approx - 0.936629, v_{2} \approx 0.936629

Evaluate

1 \times v^{4} \times 204 - 157

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

1 \times v^{4} \times 204 - 157 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times v^{4} \times 204

Rewrite the expression

v^{4} \times 204

Use the commutative property to reorder the terms

204 v^{4}

204 v^{4} - 157 = 0

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

204 v^{4} = 0 + 157

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

204 v^{4} = 157

Divide both sides

\frac{204 v ^{4}}{204} = \frac{157}{204}

Divide the numbers

v^{4} = \frac{157}{204}

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

v = \pm 4 \frac{157}{204}

Simplify the expression

More Steps

Evaluate

4 \frac{157}{204}

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

\frac{4 157}{4 204}

Multiply by the Conjugate

\frac{4 157 \times 4 20 4 ^{3}}{4 204 \times 4 20 4 ^{3}}

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

\frac{4 157 \times 20 4 ^{3}}{4 204 \times 4 20 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

4204 \times 4 20 4^{3}

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

4 204 \times 20 4^{3}

Calculate the product

4 20 4^{4}

Reduce the index of the radical and exponent with 4

204

\frac{4 157 \times 20 4 ^{3}}{204}

v = \pm \frac{4 157 \times 20 4 ^{3}}{204}

Separate the equation into 2 possible cases

v = \frac{4 157 \times 20 4 ^{3}}{204} v = - \frac{4 157 \times 20 4 ^{3}}{204}

Solution

v_{1} = - \frac{4 157 \times 20 4 ^{3}}{204}, v_{2} = \frac{4 157 \times 20 4 ^{3}}{204}

Alternative Form

v_{1} \approx - 0.936629, v_{2} \approx 0.936629

Show Solution