Solve 3(5y^6)-3 - ScanMath

Question

Simplify the expression

15 y^{6} - 3

Evaluate

3 \times 5 y^{6} - 3

Solution

15 y^{6} - 3

Show Solution

3 (5 y^{6} - 1)

Evaluate

3 \times 5 y^{6} - 3

Multiply the numbers

More Steps

Evaluate

3 \times 5

Multiply the numbers

15

Evaluate

15 y^{6}

15 y^{6} - 3

Solution

3 (5 y^{6} - 1)

Show Solution

y_{1} = - \frac{6 3125}{5}, y_{2} = \frac{6 3125}{5}

Alternative Form

y_{1} \approx - 0.764724, y_{2} \approx 0.764724

Evaluate

3 (5 y^{6}) - 3

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

3 (5 y^{6}) - 3 = 0

Multiply the terms

3 \times 5 y^{6} - 3 = 0

Multiply the numbers

15 y^{6} - 3 = 0

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

15 y^{6} = 0 + 3

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

15 y^{6} = 3

Divide both sides

\frac{15 y ^{6}}{15} = \frac{3}{15}

Divide the numbers

y^{6} = \frac{3}{15}

Cancel out the common factor 3

y^{6} = \frac{1}{5}

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

y = \pm 6 \frac{1}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{5}

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

\frac{6 1}{6 5}

Simplify the radical expression

\frac{1}{6 5}

Multiply by the Conjugate

\frac{6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 6 5^{5}

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

6 5 \times 5^{5}

Calculate the product

6 5^{6}

Reduce the index of the radical and exponent with 6

5

\frac{6 3125}{5}

y = \pm \frac{6 3125}{5}

Separate the equation into 2 possible cases

y = \frac{6 3125}{5} y = - \frac{6 3125}{5}

Solution

y_{1} = - \frac{6 3125}{5}, y_{2} = \frac{6 3125}{5}

Alternative Form

y_{1} \approx - 0.764724, y_{2} \approx 0.764724

Show Solution