Solve 4G^410-1 - ScanMath

Question

Simplify the expression

40 G^{4} - 1

Evaluate

4 G^{4} \times 10 - 1

Solution

40 G^{4} - 1

Show Solution

G_{1} = - \frac{4 250}{10}, G_{2} = \frac{4 250}{10}

Alternative Form

G_{1} \approx - 0.397635, G_{2} \approx 0.397635

Evaluate

4 G^{4} \times 10 - 1

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

4 G^{4} \times 10 - 1 = 0

Multiply the terms

40 G^{4} - 1 = 0

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

40 G^{4} = 0 + 1

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

40 G^{4} = 1

Divide both sides

\frac{40 G ^{4}}{40} = \frac{1}{40}

Divide the numbers

G^{4} = \frac{1}{40}

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

G = \pm 4 \frac{1}{40}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{40}

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

\frac{4 1}{4 40}

Simplify the radical expression

\frac{1}{4 40}

Multiply by the Conjugate

\frac{4 4 0 ^{3}}{4 40 \times 4 4 0 ^{3}}

Simplify

\frac{4 4 250}{4 40 \times 4 4 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

440 \times 4 4 0^{3}

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

4 40 \times 4 0^{3}

Calculate the product

4 4 0^{4}

Reduce the index of the radical and exponent with 4

40

\frac{4 4 250}{40}

Cancel out the common factor 4

\frac{4 250}{10}

G = \pm \frac{4 250}{10}

Separate the equation into 2 possible cases

G = \frac{4 250}{10} G = - \frac{4 250}{10}

Solution

G_{1} = - \frac{4 250}{10}, G_{2} = \frac{4 250}{10}

Alternative Form

G_{1} \approx - 0.397635, G_{2} \approx 0.397635

Show Solution