Solve 1910n^6-8 - ScanMath

Question

Factor the expression

2 (955 n^{6} - 4)

Evaluate

1910 n^{6} - 8

Solution

2 (955 n^{6} - 4)

Show Solution

n_{1} = - \frac{6 4 \times 95 5 ^{5}}{955}, n_{2} = \frac{6 4 \times 95 5 ^{5}}{955}

Alternative Form

n_{1} \approx - 0.401491, n_{2} \approx 0.401491

Evaluate

1910 n^{6} - 8

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

1910 n^{6} - 8 = 0

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

1910 n^{6} = 0 + 8

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

1910 n^{6} = 8

Divide both sides

\frac{1910 n ^{6}}{1910} = \frac{8}{1910}

Divide the numbers

n^{6} = \frac{8}{1910}

Cancel out the common factor 2

n^{6} = \frac{4}{955}

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

n = \pm 6 \frac{4}{955}

Simplify the expression

More Steps

Evaluate

6 \frac{4}{955}

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

\frac{6 4}{6 955}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

\frac{3 2}{6 955}

Multiply by the Conjugate

\frac{3 2 \times 6 95 5 ^{5}}{6 955 \times 6 95 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

32 \times 6 95 5^{5}

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

6 2^{2} \times 6 95 5^{5}

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

6 2^{2} \times 95 5^{5}

Calculate the product

6 4 \times 95 5^{5}

\frac{6 4 \times 95 5 ^{5}}{6 955 \times 6 95 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

6955 \times 6 95 5^{5}

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

6 955 \times 95 5^{5}

Calculate the product

6 95 5^{6}

Reduce the index of the radical and exponent with 6

955

\frac{6 4 \times 95 5 ^{5}}{955}

n = \pm \frac{6 4 \times 95 5 ^{5}}{955}

Separate the equation into 2 possible cases

n = \frac{6 4 \times 95 5 ^{5}}{955} n = - \frac{6 4 \times 95 5 ^{5}}{955}

Solution

n_{1} = - \frac{6 4 \times 95 5 ^{5}}{955}, n_{2} = \frac{6 4 \times 95 5 ^{5}}{955}

Alternative Form

n_{1} \approx - 0.401491, n_{2} \approx 0.401491

Show Solution