Solve 61-2n^5 - ScanMath

Question

Find the roots

n = \frac{5 976}{2}

Alternative Form

n \approx 1.980888

Evaluate

61 - 2 n^{5}

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

61 - 2 n^{5} = 0

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

- 2 n^{5} = 0 - 61

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

- 2 n^{5} = - 61

Change the signs on both sides of the equation

2 n^{5} = 61

Divide both sides

\frac{2 n ^{5}}{2} = \frac{61}{2}

Divide the numbers

n^{5} = \frac{61}{2}

Take the 5 -th root on both sides of the equation

5 n^{5} = 5 \frac{61}{2}

Calculate

n = 5 \frac{61}{2}

Solution

More Steps

Evaluate

5 \frac{61}{2}

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

\frac{5 61}{5 2}

Multiply by the Conjugate

\frac{5 61 \times 5 2 ^{4}}{5 2 \times 5 2 ^{4}}

Simplify

\frac{5 61 \times 5 16}{5 2 \times 5 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

561 \times 516

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

5 61 \times 16

Calculate the product

5976

\frac{5 976}{5 2 \times 5 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

52 \times 5 2^{4}

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

5 2 \times 2^{4}

Calculate the product

5 2^{5}

Reduce the index of the radical and exponent with 5

2

\frac{5 976}{2}

n = \frac{5 976}{2}

Alternative Form

n \approx 1.980888

Show Solution