Solve p^53-212-6 - ScanMath

Question

Simplify the expression

3 p^{5} - 218

Evaluate

p^{5} \times 3 - 212 - 6

Use the commutative property to reorder the terms

3 p^{5} - 212 - 6

Solution

3 p^{5} - 218

Show Solution

p = \frac{5 17658}{3}

Alternative Form

p \approx 2.356498

Evaluate

p^{5} \times 3 - 212 - 6

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

p^{5} \times 3 - 212 - 6 = 0

Use the commutative property to reorder the terms

3 p^{5} - 212 - 6 = 0

Subtract the numbers

3 p^{5} - 218 = 0

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

3 p^{5} = 0 + 218

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

3 p^{5} = 218

Divide both sides

\frac{3 p ^{5}}{3} = \frac{218}{3}

Divide the numbers

p^{5} = \frac{218}{3}

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

5 p^{5} = 5 \frac{218}{3}

Calculate

p = 5 \frac{218}{3}

Solution

More Steps

Evaluate

5 \frac{218}{3}

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

\frac{5 218}{5 3}

Multiply by the Conjugate

\frac{5 218 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 218 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

5218 \times 581

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

5 218 \times 81

Calculate the product

517658

\frac{5 17658}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 5 3^{4}

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

5 3 \times 3^{4}

Calculate the product

5 3^{5}

Reduce the index of the radical and exponent with 5

3

\frac{5 17658}{3}

p = \frac{5 17658}{3}

Alternative Form

p \approx 2.356498

Show Solution