Solve v^4124-16 - ScanMath

Question

Simplify the expression

124 v^{4} - 16

Evaluate

v^{4} \times 124 - 16

Solution

124 v^{4} - 16

Show Solution

4 (31 v^{4} - 4)

Evaluate

v^{4} \times 124 - 16

Use the commutative property to reorder the terms

124 v^{4} - 16

Solution

4 (31 v^{4} - 4)

Show Solution

v_{1} = - \frac{4 119164}{31}, v_{2} = \frac{4 119164}{31}

Alternative Form

v_{1} \approx - 0.599342, v_{2} \approx 0.599342

Evaluate

v^{4} \times 124 - 16

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

v^{4} \times 124 - 16 = 0

Use the commutative property to reorder the terms

124 v^{4} - 16 = 0

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

124 v^{4} = 0 + 16

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

124 v^{4} = 16

Divide both sides

\frac{124 v ^{4}}{124} = \frac{16}{124}

Divide the numbers

v^{4} = \frac{16}{124}

Cancel out the common factor 4

v^{4} = \frac{4}{31}

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

v = \pm 4 \frac{4}{31}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{31}

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

\frac{4 4}{4 31}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{4 31}

Multiply by the Conjugate

\frac{2 \times 4 3 1 ^{3}}{4 31 \times 4 3 1 ^{3}}

Simplify

\frac{2 \times 4 29791}{4 31 \times 4 3 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

2 \times 429791

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

4 2^{2} \times 429791

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

4 2^{2} \times 29791

Calculate the product

4119164

\frac{4 119164}{4 31 \times 4 3 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

431 \times 4 3 1^{3}

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

4 31 \times 3 1^{3}

Calculate the product

4 3 1^{4}

Reduce the index of the radical and exponent with 4

31

\frac{4 119164}{31}

v = \pm \frac{4 119164}{31}

Separate the equation into 2 possible cases

v = \frac{4 119164}{31} v = - \frac{4 119164}{31}

Solution

v_{1} = - \frac{4 119164}{31}, v_{2} = \frac{4 119164}{31}

Alternative Form

v_{1} \approx - 0.599342, v_{2} \approx 0.599342

Show Solution