Solve 3d^427-747 - ScanMath

Question

Simplify the expression

81 d^{4} - 747

Evaluate

3 d^{4} \times 27 - 747

Solution

81 d^{4} - 747

Show Solution

9 (9 d^{4} - 83)

Evaluate

3 d^{4} \times 27 - 747

Multiply the terms

81 d^{4} - 747

Solution

9 (9 d^{4} - 83)

Show Solution

d_{1} = - \frac{4 747}{3}, d_{2} = \frac{4 747}{3}

Alternative Form

d_{1} \approx - 1.742645, d_{2} \approx 1.742645

Evaluate

3 d^{4} \times 27 - 747

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

3 d^{4} \times 27 - 747 = 0

Multiply the terms

81 d^{4} - 747 = 0

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

81 d^{4} = 0 + 747

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

81 d^{4} = 747

Divide both sides

\frac{81 d ^{4}}{81} = \frac{747}{81}

Divide the numbers

d^{4} = \frac{747}{81}

Cancel out the common factor 9

d^{4} = \frac{83}{9}

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

d = \pm 4 \frac{83}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{83}{9}

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

\frac{4 83}{4 9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{4 83}{3}

Multiply by the Conjugate

\frac{4 83 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

483 \times 3

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

483 \times 4 3^{2}

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

4 83 \times 3^{2}

Calculate the product

4747

\frac{4 747}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 747}{3}

d = \pm \frac{4 747}{3}

Separate the equation into 2 possible cases

d = \frac{4 747}{3} d = - \frac{4 747}{3}

Solution

d_{1} = - \frac{4 747}{3}, d_{2} = \frac{4 747}{3}

Alternative Form

d_{1} \approx - 1.742645, d_{2} \approx 1.742645

Show Solution