Solve p^24048-1 - ScanMath

Question

Simplify the expression

4048 p^{2} - 1

Evaluate

p^{2} \times 4048 - 1

Solution

4048 p^{2} - 1

Show Solution

p_{1} = - \frac{253}{1012}, p_{2} = \frac{253}{1012}

Alternative Form

p_{1} \approx - 0.015717, p_{2} \approx 0.015717

Evaluate

p^{2} \times 4048 - 1

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

p^{2} \times 4048 - 1 = 0

Use the commutative property to reorder the terms

4048 p^{2} - 1 = 0

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

4048 p^{2} = 0 + 1

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

4048 p^{2} = 1

Divide both sides

\frac{4048 p ^{2}}{4048} = \frac{1}{4048}

Divide the numbers

p^{2} = \frac{1}{4048}

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

p = \pm \frac{1}{4048}

Simplify the expression

More Steps

Evaluate

\frac{1}{4048}

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

\frac{1}{4048}

Simplify the radical expression

\frac{1}{4048}

Simplify the radical expression

More Steps

Evaluate

4048

Write the expression as a product where the root of one of the factors can be evaluated

16 \times 253

Write the number in exponential form with the base of 4

4^{2} \times 253

The root of a product is equal to the product of the roots of each factor

4^{2} \times 253

Reduce the index of the radical and exponent with 2

4253

\frac{1}{4 253}

Multiply by the Conjugate

\frac{253}{4 253 \times 253}

Multiply the numbers

More Steps

Evaluate

4253 \times 253

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

4 \times 253

Multiply the terms

1012

\frac{253}{1012}

p = \pm \frac{253}{1012}

Separate the equation into 2 possible cases

p = \frac{253}{1012} p = - \frac{253}{1012}

Solution

p_{1} = - \frac{253}{1012}, p_{2} = \frac{253}{1012}

Alternative Form

p_{1} \approx - 0.015717, p_{2} \approx 0.015717

Show Solution