Solve 100r^4-12 - ScanMath

Question

Factor the expression

4 (25 r^{4} - 3)

Evaluate

100 r^{4} - 12

Solution

4 (25 r^{4} - 3)

Show Solution

r_{1} = - \frac{4 75}{5}, r_{2} = \frac{4 75}{5}

Alternative Form

r_{1} \approx - 0.588566, r_{2} \approx 0.588566

Evaluate

100 r^{4} - 12

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

100 r^{4} - 12 = 0

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

100 r^{4} = 0 + 12

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

100 r^{4} = 12

Divide both sides

\frac{100 r ^{4}}{100} = \frac{12}{100}

Divide the numbers

r^{4} = \frac{12}{100}

Cancel out the common factor 4

r^{4} = \frac{3}{25}

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

r = \pm 4 \frac{3}{25}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{25}

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

\frac{4 3}{4 25}

Simplify the radical expression

More Steps

Evaluate

425

Write the number in exponential form with the base of 5

4 5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{4 3}{5}

Multiply by the Conjugate

\frac{4 3 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

43 \times 5

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

43 \times 4 5^{2}

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

4 3 \times 5^{2}

Calculate the product

475

\frac{4 75}{5 \times 5}

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

\frac{4 75}{5}

r = \pm \frac{4 75}{5}

Separate the equation into 2 possible cases

r = \frac{4 75}{5} r = - \frac{4 75}{5}

Solution

r_{1} = - \frac{4 75}{5}, r_{2} = \frac{4 75}{5}

Alternative Form

r_{1} \approx - 0.588566, r_{2} \approx 0.588566

Show Solution