Solve k^58-36-1 - ScanMath

Question

Simplify the expression

8 k^{5} - 37

Evaluate

k^{5} \times 8 - 36 - 1

Use the commutative property to reorder the terms

8 k^{5} - 36 - 1

Solution

8 k^{5} - 37

Show Solution

k = \frac{5 148}{2}

Alternative Form

k \approx 1.358383

Evaluate

k^{5} \times 8 - 36 - 1

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

k^{5} \times 8 - 36 - 1 = 0

Use the commutative property to reorder the terms

8 k^{5} - 36 - 1 = 0

Subtract the numbers

8 k^{5} - 37 = 0

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

8 k^{5} = 0 + 37

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

8 k^{5} = 37

Divide both sides

\frac{8 k ^{5}}{8} = \frac{37}{8}

Divide the numbers

k^{5} = \frac{37}{8}

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

5 k^{5} = 5 \frac{37}{8}

Calculate

k = 5 \frac{37}{8}

Solution

More Steps

Evaluate

5 \frac{37}{8}

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

\frac{5 37}{5 8}

Multiply by the Conjugate

\frac{5 37 \times 5 8 ^{4}}{5 8 \times 5 8 ^{4}}

Simplify

\frac{5 37 \times 2 ^{2} 5 4}{5 8 \times 5 8 ^{4}}

Multiply the numbers

More Steps

Evaluate

537 \times 2^{2} 54

Multiply the terms

5148 \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 5148

\frac{2 ^{2} 5 148}{5 8 \times 5 8 ^{4}}

Multiply the numbers

More Steps

Evaluate

58 \times 5 8^{4}

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

5 8 \times 8^{4}

Calculate the product

5 8^{5}

Transform the expression

5 2^{15}

Reduce the index of the radical and exponent with 5

2^{3}

\frac{2 ^{2} 5 148}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{5 148}{2}

k = \frac{5 148}{2}

Alternative Form

k \approx 1.358383

Show Solution