Solve r^4312-36 - ScanMath

Question

Simplify the expression

312 r^{4} - 36

Evaluate

r^{4} \times 312 - 36

Solution

312 r^{4} - 36

Show Solution

12 (26 r^{4} - 3)

Evaluate

r^{4} \times 312 - 36

Use the commutative property to reorder the terms

312 r^{4} - 36

Solution

12 (26 r^{4} - 3)

Show Solution

r_{1} = - \frac{4 52728}{26}, r_{2} = \frac{4 52728}{26}

Alternative Form

r_{1} \approx - 0.582823, r_{2} \approx 0.582823

Evaluate

r^{4} \times 312 - 36

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

r^{4} \times 312 - 36 = 0

Use the commutative property to reorder the terms

312 r^{4} - 36 = 0

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

312 r^{4} = 0 + 36

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

312 r^{4} = 36

Divide both sides

\frac{312 r ^{4}}{312} = \frac{36}{312}

Divide the numbers

r^{4} = \frac{36}{312}

Cancel out the common factor 12

r^{4} = \frac{3}{26}

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

r = \pm 4 \frac{3}{26}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{26}

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

\frac{4 3}{4 26}

Multiply by the Conjugate

\frac{4 3 \times 4 2 6 ^{3}}{4 26 \times 4 2 6 ^{3}}

Simplify

\frac{4 3 \times 4 17576}{4 26 \times 4 2 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 417576

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

4 3 \times 17576

Calculate the product

452728

\frac{4 52728}{4 26 \times 4 2 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

426 \times 4 2 6^{3}

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

4 26 \times 2 6^{3}

Calculate the product

4 2 6^{4}

Reduce the index of the radical and exponent with 4

26

\frac{4 52728}{26}

r = \pm \frac{4 52728}{26}

Separate the equation into 2 possible cases

r = \frac{4 52728}{26} r = - \frac{4 52728}{26}

Solution

r_{1} = - \frac{4 52728}{26}, r_{2} = \frac{4 52728}{26}

Alternative Form

r_{1} \approx - 0.582823, r_{2} \approx 0.582823

Show Solution