Solve 1d^630-125 - ScanMath

Question

Simplify the expression

Solution

30 d^{6} - 125

Evaluate

1 \times d^{6} \times 30 - 125

Solution

More Steps

Evaluate

1 \times d^{6} \times 30

Rewrite the expression

d^{6} \times 30

Use the commutative property to reorder the terms

30 d^{6}

30 d^{6} - 125

Show Solution

Factor the expression

Factor

5 (6 d^{6} - 25)

Evaluate

1 \times d^{6} \times 30 - 125

Multiply the terms

More Steps

Evaluate

1 \times d^{6} \times 30

Rewrite the expression

d^{6} \times 30

Use the commutative property to reorder the terms

30 d^{6}

30 d^{6} - 125

Solution

5 (6 d^{6} - 25)

Show Solution

Find the roots

Find the roots of the algebra expression

d_{1} = - \frac{6 194400}{6}, d_{2} = \frac{6 194400}{6}

Alternative Form

d_{1} \approx - 1.268522, d_{2} \approx 1.268522

Evaluate

1 \times d^{6} \times 30 - 125

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

1 \times d^{6} \times 30 - 125 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times d^{6} \times 30

Rewrite the expression

d^{6} \times 30

Use the commutative property to reorder the terms

30 d^{6}

30 d^{6} - 125 = 0

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

30 d^{6} = 0 + 125

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

30 d^{6} = 125

Divide both sides

\frac{30 d ^{6}}{30} = \frac{125}{30}

Divide the numbers

d^{6} = \frac{125}{30}

Cancel out the common factor 5

d^{6} = \frac{25}{6}

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

d = \pm 6 \frac{25}{6}

Simplify the expression

More Steps

Evaluate

6 \frac{25}{6}

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

\frac{6 25}{6 6}

Simplify the radical expression

More Steps

Evaluate

625

Write the number in exponential form with the base of 5

6 5^{2}

Reduce the index of the radical and exponent with 2

35

\frac{3 5}{6 6}

Multiply by the Conjugate

\frac{3 5 \times 6 6 ^{5}}{6 6 \times 6 6 ^{5}}

Simplify

\frac{3 5 \times 6 7776}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

35 \times 67776

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

6 5^{2} \times 67776

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

6 5^{2} \times 7776

Calculate the product

6194400

\frac{6 194400}{6 6 \times 6 6 ^{5}}

Multiply the numbers

More Steps

Evaluate

66 \times 6 6^{5}

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

6 6 \times 6^{5}

Calculate the product

6 6^{6}

Reduce the index of the radical and exponent with 6

6

\frac{6 194400}{6}

d = \pm \frac{6 194400}{6}

Separate the equation into 2 possible cases

d = \frac{6 194400}{6} d = - \frac{6 194400}{6}

Solution

d_{1} = - \frac{6 194400}{6}, d_{2} = \frac{6 194400}{6}

Alternative Form

d_{1} \approx - 1.268522, d_{2} \approx 1.268522

Show Solution

1d^630 125

Simplify the expression

Factor the expression

Find the roots