Solve v^53-63-1 - ScanMath

Question

Simplify the expression

3 v^{5} - 64

Evaluate

v^{5} \times 3 - 63 - 1

Use the commutative property to reorder the terms

3 v^{5} - 63 - 1

Solution

3 v^{5} - 64

Show Solution

v = \frac{2 5 162}{3}

Alternative Form

v \approx 1.844216

Evaluate

v^{5} \times 3 - 63 - 1

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

v^{5} \times 3 - 63 - 1 = 0

Use the commutative property to reorder the terms

3 v^{5} - 63 - 1 = 0

Subtract the numbers

3 v^{5} - 64 = 0

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

3 v^{5} = 0 + 64

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

3 v^{5} = 64

Divide both sides

\frac{3 v ^{5}}{3} = \frac{64}{3}

Divide the numbers

v^{5} = \frac{64}{3}

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

5 v^{5} = 5 \frac{64}{3}

Calculate

v = 5 \frac{64}{3}

Solution

More Steps

Evaluate

5 \frac{64}{3}

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

\frac{5 64}{5 3}

Simplify the radical expression

More Steps

Evaluate

564

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

5 32 \times 2

Write the number in exponential form with the base of 2

5 2^{5} \times 2

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

5 2^{5} \times 52

Reduce the index of the radical and exponent with 5

252

\frac{2 5 2}{5 3}

Multiply by the Conjugate

\frac{2 5 2 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{2 5 2 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

52 \times 581

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

5 2 \times 81

Calculate the product

5162

\frac{2 5 162}{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{2 5 162}{3}

v = \frac{2 5 162}{3}

Alternative Form

v \approx 1.844216

Show Solution