Solve k^36-97-14 - ScanMath

Question

Simplify the expression

Solution

6 k^{3} - 111

Evaluate

k^{3} \times 6 - 97 - 14

Use the commutative property to reorder the terms

6 k^{3} - 97 - 14

Solution

6 k^{3} - 111

Show Solution

Factor the expression

Factor

3 (2 k^{3} - 37)

Evaluate

k^{3} \times 6 - 97 - 14

Use the commutative property to reorder the terms

6 k^{3} - 97 - 14

Subtract the numbers

6 k^{3} - 111

Solution

3 (2 k^{3} - 37)

Show Solution

Find the roots

Find the roots of the algebra expression

k = \frac{3 148}{2}

Alternative Form

k \approx 2.644786

Evaluate

k^{3} \times 6 - 97 - 14

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

k^{3} \times 6 - 97 - 14 = 0

Use the commutative property to reorder the terms

6 k^{3} - 97 - 14 = 0

Subtract the numbers

6 k^{3} - 111 = 0

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

6 k^{3} = 0 + 111

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

6 k^{3} = 111

Divide both sides

\frac{6 k ^{3}}{6} = \frac{111}{6}

Divide the numbers

k^{3} = \frac{111}{6}

Cancel out the common factor 3

k^{3} = \frac{37}{2}

Take the 3 -th root on both sides of the equation

3 k^{3} = 3 \frac{37}{2}

Calculate

k = 3 \frac{37}{2}

Solution

More Steps

Evaluate

3 \frac{37}{2}

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

\frac{3 37}{3 2}

Multiply by the Conjugate

\frac{3 37 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 37 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

337 \times 34

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

3 37 \times 4

Calculate the product

3148

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

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 148}{2}

k = \frac{3 148}{2}

Alternative Form

k \approx 2.644786

Show Solution

K^36 97 14

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression