Solve p^40092-36 - ScanMath

Question

Simplify the expression

92 p^{4} - 36

Evaluate

p^{4} \times 92 - 36

Solution

92 p^{4} - 36

Show Solution

4 (23 p^{4} - 9)

Evaluate

p^{4} \times 92 - 36

Use the commutative property to reorder the terms

92 p^{4} - 36

Solution

4 (23 p^{4} - 9)

Show Solution

p_{1} = - \frac{4 109503}{23}, p_{2} = \frac{4 109503}{23}

Alternative Form

p_{1} \approx - 0.790913, p_{2} \approx 0.790913

Evaluate

p^{4} \times 92 - 36

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

p^{4} \times 92 - 36 = 0

Use the commutative property to reorder the terms

92 p^{4} - 36 = 0

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

92 p^{4} = 0 + 36

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

92 p^{4} = 36

Divide both sides

\frac{92 p ^{4}}{92} = \frac{36}{92}

Divide the numbers

p^{4} = \frac{36}{92}

Cancel out the common factor 4

p^{4} = \frac{9}{23}

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

p = \pm 4 \frac{9}{23}

Simplify the expression

More Steps

Evaluate

4 \frac{9}{23}

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

\frac{4 9}{4 23}

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{3}{4 23}

Multiply by the Conjugate

\frac{3 \times 4 2 3 ^{3}}{4 23 \times 4 2 3 ^{3}}

Simplify

\frac{3 \times 4 12167}{4 23 \times 4 2 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

3 \times 412167

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

4 3^{2} \times 412167

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

4 3^{2} \times 12167

Calculate the product

4109503

\frac{4 109503}{4 23 \times 4 2 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

423 \times 4 2 3^{3}

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

4 23 \times 2 3^{3}

Calculate the product

4 2 3^{4}

Reduce the index of the radical and exponent with 4

23

\frac{4 109503}{23}

p = \pm \frac{4 109503}{23}

Separate the equation into 2 possible cases

p = \frac{4 109503}{23} p = - \frac{4 109503}{23}

Solution

p_{1} = - \frac{4 109503}{23}, p_{2} = \frac{4 109503}{23}

Alternative Form

p_{1} \approx - 0.790913, p_{2} \approx 0.790913

Show Solution