Solve g^4212-60008

Question

Simplify the expression

212 g^{4} - 60008

Evaluate

g^{4} \times 212 - 60008

Solution

212 g^{4} - 60008

Show Solution

4 (53 g^{4} - 15002)

Evaluate

g^{4} \times 212 - 60008

Use the commutative property to reorder the terms

212 g^{4} - 60008

Solution

4 (53 g^{4} - 15002)

Show Solution

g_{1} = - \frac{4 15002 \times 5 3 ^{3}}{53}, g_{2} = \frac{4 15002 \times 5 3 ^{3}}{53}

Alternative Form

g_{1} \approx - 4.101742, g_{2} \approx 4.101742

Evaluate

g^{4} \times 212 - 60008

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

g^{4} \times 212 - 60008 = 0

Use the commutative property to reorder the terms

212 g^{4} - 60008 = 0

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

212 g^{4} = 0 + 60008

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

212 g^{4} = 60008

Divide both sides

\frac{212 g ^{4}}{212} = \frac{60008}{212}

Divide the numbers

g^{4} = \frac{60008}{212}

Cancel out the common factor 4

g^{4} = \frac{15002}{53}

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

g = \pm 4 \frac{15002}{53}

Simplify the expression

More Steps

Evaluate

4 \frac{15002}{53}

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

\frac{4 15002}{4 53}

Multiply by the Conjugate

\frac{4 15002 \times 4 5 3 ^{3}}{4 53 \times 4 5 3 ^{3}}

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

\frac{4 15002 \times 5 3 ^{3}}{4 53 \times 4 5 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

453 \times 4 5 3^{3}

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

4 53 \times 5 3^{3}

Calculate the product

4 5 3^{4}

Reduce the index of the radical and exponent with 4

53

\frac{4 15002 \times 5 3 ^{3}}{53}

g = \pm \frac{4 15002 \times 5 3 ^{3}}{53}

Separate the equation into 2 possible cases

g = \frac{4 15002 \times 5 3 ^{3}}{53} g = - \frac{4 15002 \times 5 3 ^{3}}{53}

Solution

g_{1} = - \frac{4 15002 \times 5 3 ^{3}}{53}, g_{2} = \frac{4 15002 \times 5 3 ^{3}}{53}

Alternative Form

g_{1} \approx - 4.101742, g_{2} \approx 4.101742

Show Solution