Solve dd^5003-10 - ScanMath

Question

Simplify the expression

3 d^{6} - 10

Evaluate

d \times d^{5} \times 3 - 10

Solution

More Steps

Evaluate

d \times d^{5} \times 3

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 3

Add the numbers

d^{6} \times 3

Use the commutative property to reorder the terms

3 d^{6}

3 d^{6} - 10

Show Solution

d_{1} = - \frac{6 2430}{3}, d_{2} = \frac{6 2430}{3}

Alternative Form

d_{1} \approx - 1.222212, d_{2} \approx 1.222212

Evaluate

d \times d^{5} \times 3 - 10

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

d \times d^{5} \times 3 - 10 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 3

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 3

Add the numbers

d^{6} \times 3

Use the commutative property to reorder the terms

3 d^{6}

3 d^{6} - 10 = 0

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

3 d^{6} = 0 + 10

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

3 d^{6} = 10

Divide both sides

\frac{3 d ^{6}}{3} = \frac{10}{3}

Divide the numbers

d^{6} = \frac{10}{3}

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

d = \pm 6 \frac{10}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{10}{3}

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

\frac{6 10}{6 3}

Multiply by the Conjugate

\frac{6 10 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 10 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

610 \times 6243

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

6 10 \times 243

Calculate the product

62430

\frac{6 2430}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 6 3^{5}

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

6 3 \times 3^{5}

Calculate the product

6 3^{6}

Reduce the index of the radical and exponent with 6

3

\frac{6 2430}{3}

d = \pm \frac{6 2430}{3}

Separate the equation into 2 possible cases

d = \frac{6 2430}{3} d = - \frac{6 2430}{3}

Solution

d_{1} = - \frac{6 2430}{3}, d_{2} = \frac{6 2430}{3}

Alternative Form

d_{1} \approx - 1.222212, d_{2} \approx 1.222212

Show Solution