Solve 6t^5-10 - ScanMath

Question

Factor the expression

2 (3 t^{5} - 5)

Evaluate

6 t^{5} - 10

Solution

2 (3 t^{5} - 5)

Show Solution

t = \frac{5 405}{3}

Alternative Form

t \approx 1.107566

Evaluate

6 t^{5} - 10

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

6 t^{5} - 10 = 0

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

6 t^{5} = 0 + 10

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

6 t^{5} = 10

Divide both sides

\frac{6 t ^{5}}{6} = \frac{10}{6}

Divide the numbers

t^{5} = \frac{10}{6}

Cancel out the common factor 2

t^{5} = \frac{5}{3}

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

5 t^{5} = 5 \frac{5}{3}

Calculate

t = 5 \frac{5}{3}

Solution

More Steps

Evaluate

5 \frac{5}{3}

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

\frac{5 5}{5 3}

Multiply by the Conjugate

\frac{5 5 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 5 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

55 \times 581

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

5 5 \times 81

Calculate the product

5405

\frac{5 405}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 5 3^{4}

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

5 3 \times 3^{4}

Calculate the product

5 3^{5}

Reduce the index of the radical and exponent with 5

3

\frac{5 405}{3}

t = \frac{5 405}{3}

Alternative Form

t \approx 1.107566

Show Solution