Solve p^4620-63001

Question

Simplify the expression

620 p^{4} - 63001

Evaluate

p^{4} \times 620 - 63001

Solution

620 p^{4} - 63001

Show Solution

p_{1} = - \frac{4 63001 \times 62 0 ^{3}}{620}, p_{2} = \frac{4 63001 \times 62 0 ^{3}}{620}

Alternative Form

p_{1} \approx - 3.174965, p_{2} \approx 3.174965

Evaluate

p^{4} \times 620 - 63001

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

p^{4} \times 620 - 63001 = 0

Use the commutative property to reorder the terms

620 p^{4} - 63001 = 0

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

620 p^{4} = 0 + 63001

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

620 p^{4} = 63001

Divide both sides

\frac{620 p ^{4}}{620} = \frac{63001}{620}

Divide the numbers

p^{4} = \frac{63001}{620}

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

p = \pm 4 \frac{63001}{620}

Simplify the expression

More Steps

Evaluate

4 \frac{63001}{620}

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

\frac{4 63001}{4 620}

Simplify the radical expression

More Steps

Evaluate

463001

Write the number in exponential form with the base of 251

4 25 1^{2}

Reduce the index of the radical and exponent with 2

251

\frac{251}{4 620}

Multiply by the Conjugate

\frac{251 \times 4 62 0 ^{3}}{4 620 \times 4 62 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

251 \times 4 62 0^{3}

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

4 25 1^{2} \times 4 62 0^{3}

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

4 25 1^{2} \times 62 0^{3}

Calculate the product

4 63001 \times 62 0^{3}

\frac{4 63001 \times 62 0 ^{3}}{4 620 \times 4 62 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

4620 \times 4 62 0^{3}

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

4 620 \times 62 0^{3}

Calculate the product

4 62 0^{4}

Reduce the index of the radical and exponent with 4

620

\frac{4 63001 \times 62 0 ^{3}}{620}

p = \pm \frac{4 63001 \times 62 0 ^{3}}{620}

Separate the equation into 2 possible cases

p = \frac{4 63001 \times 62 0 ^{3}}{620} p = - \frac{4 63001 \times 62 0 ^{3}}{620}

Solution

p_{1} = - \frac{4 63001 \times 62 0 ^{3}}{620}, p_{2} = \frac{4 63001 \times 62 0 ^{3}}{620}

Alternative Form

p_{1} \approx - 3.174965, p_{2} \approx 3.174965

Show Solution