Solve p^4623-60001

Question

Simplify the expression

623 p^{4} - 60001

Evaluate

p^{4} \times 623 - 60001

Solution

623 p^{4} - 60001

Show Solution

p_{1} = - \frac{4 60001 \times 62 3 ^{3}}{623}, p_{2} = \frac{4 60001 \times 62 3 ^{3}}{623}

Alternative Form

p_{1} \approx - 3.132691, p_{2} \approx 3.132691

Evaluate

p^{4} \times 623 - 60001

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

p^{4} \times 623 - 60001 = 0

Use the commutative property to reorder the terms

623 p^{4} - 60001 = 0

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

623 p^{4} = 0 + 60001

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

623 p^{4} = 60001

Divide both sides

\frac{623 p ^{4}}{623} = \frac{60001}{623}

Divide the numbers

p^{4} = \frac{60001}{623}

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

p = \pm 4 \frac{60001}{623}

Simplify the expression

More Steps

Evaluate

4 \frac{60001}{623}

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

\frac{4 60001}{4 623}

Multiply by the Conjugate

\frac{4 60001 \times 4 62 3 ^{3}}{4 623 \times 4 62 3 ^{3}}

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

\frac{4 60001 \times 62 3 ^{3}}{4 623 \times 4 62 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

4623 \times 4 62 3^{3}

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

4 623 \times 62 3^{3}

Calculate the product

4 62 3^{4}

Reduce the index of the radical and exponent with 4

623

\frac{4 60001 \times 62 3 ^{3}}{623}

p = \pm \frac{4 60001 \times 62 3 ^{3}}{623}

Separate the equation into 2 possible cases

p = \frac{4 60001 \times 62 3 ^{3}}{623} p = - \frac{4 60001 \times 62 3 ^{3}}{623}

Solution

p_{1} = - \frac{4 60001 \times 62 3 ^{3}}{623}, p_{2} = \frac{4 60001 \times 62 3 ^{3}}{623}

Alternative Form

p_{1} \approx - 3.132691, p_{2} \approx 3.132691

Show Solution