Solve d^5025-60001

Question

Simplify the expression

25 d^{5} - 60001

Evaluate

d^{5} \times 25 - 60001

Solution

25 d^{5} - 60001

Show Solution

d = \frac{5 7500125}{5}

Alternative Form

d \approx 4.742897

Evaluate

d^{5} \times 25 - 60001

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

d^{5} \times 25 - 60001 = 0

Use the commutative property to reorder the terms

25 d^{5} - 60001 = 0

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

25 d^{5} = 0 + 60001

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

25 d^{5} = 60001

Divide both sides

\frac{25 d ^{5}}{25} = \frac{60001}{25}

Divide the numbers

d^{5} = \frac{60001}{25}

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

5 d^{5} = 5 \frac{60001}{25}

Calculate

d = 5 \frac{60001}{25}

Solution

More Steps

Evaluate

5 \frac{60001}{25}

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

\frac{5 60001}{5 25}

Multiply by the Conjugate

\frac{5 60001 \times 5 2 5 ^{4}}{5 25 \times 5 2 5 ^{4}}

Simplify

\frac{5 60001 \times 5 5 125}{5 25 \times 5 2 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

560001 \times 55125

Multiply the terms

57500125 \times 5

Use the commutative property to reorder the terms

557500125

\frac{5 5 7500125}{5 25 \times 5 2 5 ^{4}}

Multiply the numbers

More Steps

Evaluate

525 \times 5 2 5^{4}

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

5 25 \times 2 5^{4}

Calculate the product

5 2 5^{5}

Transform the expression

5 5^{10}

Reduce the index of the radical and exponent with 5

5^{2}

\frac{5 5 7500125}{5 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{5}{5 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{5 ^{2 - 1}}

Subtract the terms

\frac{1}{5 ^{1}}

Simplify

\frac{1}{5}

\frac{5 7500125}{5}

d = \frac{5 7500125}{5}

Alternative Form

d \approx 4.742897

Show Solution