Solve n8n-pi - ScanMath

Question

Simplify the expression

8 n^{2} - π

Evaluate

n \times 8 n - π

Solution

More Steps

Evaluate

n \times 8 n

Multiply the terms

n^{2} \times 8

Use the commutative property to reorder the terms

8 n^{2}

8 n^{2} - π

Show Solution

n_{1} = - \frac{2 π}{4}, n_{2} = \frac{2 π}{4}

Alternative Form

n_{1} \approx - 0.626657, n_{2} \approx 0.626657

Evaluate

n \times 8 n - π

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

n \times 8 n - π = 0

Multiply

More Steps

Multiply the terms

n \times 8 n

Multiply the terms

n^{2} \times 8

Use the commutative property to reorder the terms

8 n^{2}

8 n^{2} - π = 0

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

8 n^{2} = 0 + π

Add the terms

8 n^{2} = π

Divide both sides

\frac{8 n ^{2}}{8} = \frac{π}{8}

Divide the numbers

n^{2} = \frac{π}{8}

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

n = \pm \frac{π}{8}

Simplify the expression

More Steps

Evaluate

\frac{π}{8}

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

\frac{π}{8}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{π}{2 2}

Multiply by the Conjugate

\frac{π \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

π \times 2

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

π \times 2

Calculate the product

2 π

\frac{2 π}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

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

2 \times 2

Multiply the numbers

4

\frac{2 π}{4}

n = \pm \frac{2 π}{4}

Separate the equation into 2 possible cases

n = \frac{2 π}{4} n = - \frac{2 π}{4}

Solution

n_{1} = - \frac{2 π}{4}, n_{2} = \frac{2 π}{4}

Alternative Form

n_{1} \approx - 0.626657, n_{2} \approx 0.626657

Show Solution