Solve r^4624-1 - ScanMath

Question

Simplify the expression

624 r^{4} - 1

Evaluate

r^{4} \times 624 - 1

Solution

624 r^{4} - 1

Show Solution

r_{1} = - \frac{4 59319}{78}, r_{2} = \frac{4 59319}{78}

Alternative Form

r_{1} \approx - 0.20008, r_{2} \approx 0.20008

Evaluate

r^{4} \times 624 - 1

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

r^{4} \times 624 - 1 = 0

Use the commutative property to reorder the terms

624 r^{4} - 1 = 0

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

624 r^{4} = 0 + 1

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

624 r^{4} = 1

Divide both sides

\frac{624 r ^{4}}{624} = \frac{1}{624}

Divide the numbers

r^{4} = \frac{1}{624}

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

r = \pm 4 \frac{1}{624}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{624}

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

\frac{4 1}{4 624}

Simplify the radical expression

\frac{1}{4 624}

Simplify the radical expression

More Steps

Evaluate

4624

Write the expression as a product where the root of one of the factors can be evaluated

4 16 \times 39

Write the number in exponential form with the base of 2

4 2^{4} \times 39

The root of a product is equal to the product of the roots of each factor

4 2^{4} \times 439

Reduce the index of the radical and exponent with 4

2439

\frac{1}{2 4 39}

Multiply by the Conjugate

\frac{4 3 9 ^{3}}{2 4 39 \times 4 3 9 ^{3}}

Simplify

\frac{4 59319}{2 4 39 \times 4 3 9 ^{3}}

Multiply the numbers

More Steps

Evaluate

2439 \times 4 3 9^{3}

Multiply the terms

2 \times 39

Multiply the terms

78

\frac{4 59319}{78}

r = \pm \frac{4 59319}{78}

Separate the equation into 2 possible cases

r = \frac{4 59319}{78} r = - \frac{4 59319}{78}

Solution

r_{1} = - \frac{4 59319}{78}, r_{2} = \frac{4 59319}{78}

Alternative Form

r_{1} \approx - 0.20008, r_{2} \approx 0.20008

Show Solution