Solve p^5498-67001 - Socratic AI (ScanMath)

Question

Simplify the expression

498 p^{5} - 67001

Evaluate

p^{5} \times 498 - 67001

Solution

498 p^{5} - 67001

Show Solution

p = \frac{5 67001 \times 49 8 ^{4}}{498}

Alternative Form

p \approx 2.665449

Evaluate

p^{5} \times 498 - 67001

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

p^{5} \times 498 - 67001 = 0

Use the commutative property to reorder the terms

498 p^{5} - 67001 = 0

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

498 p^{5} = 0 + 67001

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

498 p^{5} = 67001

Divide both sides

\frac{498 p ^{5}}{498} = \frac{67001}{498}

Divide the numbers

p^{5} = \frac{67001}{498}

Take the 5 -th root on both sides of the equation

5 p^{5} = 5 \frac{67001}{498}

Calculate

p = 5 \frac{67001}{498}

Solution

More Steps

Evaluate

5 \frac{67001}{498}

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

\frac{5 67001}{5 498}

Multiply by the Conjugate

\frac{5 67001 \times 5 49 8 ^{4}}{5 498 \times 5 49 8 ^{4}}

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

\frac{5 67001 \times 49 8 ^{4}}{5 498 \times 5 49 8 ^{4}}

Multiply the numbers

More Steps

Evaluate

5498 \times 5 49 8^{4}

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

5 498 \times 49 8^{4}

Calculate the product

5 49 8^{5}

Reduce the index of the radical and exponent with 5

498

\frac{5 67001 \times 49 8 ^{4}}{498}

p = \frac{5 67001 \times 49 8 ^{4}}{498}

Alternative Form

p \approx 2.665449

Show Solution