Solve dd^3223-100

Question

Simplify the expression

223 d^{4} - 100

Evaluate

d \times d^{3} \times 223 - 100

Solution

More Steps

Evaluate

d \times d^{3} \times 223

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 223

Add the numbers

d^{4} \times 223

Use the commutative property to reorder the terms

223 d^{4}

223 d^{4} - 100

Show Solution

d_{1} = - \frac{4 100 \times 22 3 ^{3}}{223}, d_{2} = \frac{4 100 \times 22 3 ^{3}}{223}

Alternative Form

d_{1} \approx - 0.818321, d_{2} \approx 0.818321

Evaluate

d \times d^{3} \times 223 - 100

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

d \times d^{3} \times 223 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 223

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 223

Add the numbers

d^{4} \times 223

Use the commutative property to reorder the terms

223 d^{4}

223 d^{4} - 100 = 0

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

223 d^{4} = 0 + 100

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

223 d^{4} = 100

Divide both sides

\frac{223 d ^{4}}{223} = \frac{100}{223}

Divide the numbers

d^{4} = \frac{100}{223}

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

d = \pm 4 \frac{100}{223}

Simplify the expression

More Steps

Evaluate

4 \frac{100}{223}

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

\frac{4 100}{4 223}

Simplify the radical expression

\frac{10}{4 223}

Multiply by the Conjugate

\frac{10 \times 4 22 3 ^{3}}{4 223 \times 4 22 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

10 \times 4 22 3^{3}

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

4 1 0^{2} \times 4 22 3^{3}

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

4 1 0^{2} \times 22 3^{3}

Calculate the product

4 100 \times 22 3^{3}

\frac{4 100 \times 22 3 ^{3}}{4 223 \times 4 22 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

4223 \times 4 22 3^{3}

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

4 223 \times 22 3^{3}

Calculate the product

4 22 3^{4}

Reduce the index of the radical and exponent with 4

223

\frac{4 100 \times 22 3 ^{3}}{223}

d = \pm \frac{4 100 \times 22 3 ^{3}}{223}

Separate the equation into 2 possible cases

d = \frac{4 100 \times 22 3 ^{3}}{223} d = - \frac{4 100 \times 22 3 ^{3}}{223}

Solution

d_{1} = - \frac{4 100 \times 22 3 ^{3}}{223}, d_{2} = \frac{4 100 \times 22 3 ^{3}}{223}

Alternative Form

d_{1} \approx - 0.818321, d_{2} \approx 0.818321

Show Solution