Solve k^6992-36 - ScanMath

Question

Simplify the expression

Solution

992 k^{6} - 36

Evaluate

k^{6} \times 992 - 36

Solution

992 k^{6} - 36

Show Solution

Factor the expression

Factor

4 (248 k^{6} - 9)

Evaluate

k^{6} \times 992 - 36

Use the commutative property to reorder the terms

992 k^{6} - 36

Solution

4 (248 k^{6} - 9)

Show Solution

Find the roots

Find the roots of the algebra expression

k_{1} = - \frac{6 9 \times 24 8 ^{5}}{248}, k_{2} = \frac{6 9 \times 24 8 ^{5}}{248}

Alternative Form

k_{1} \approx - 0.575394, k_{2} \approx 0.575394

Evaluate

k^{6} \times 992 - 36

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

k^{6} \times 992 - 36 = 0

Use the commutative property to reorder the terms

992 k^{6} - 36 = 0

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

992 k^{6} = 0 + 36

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

992 k^{6} = 36

Divide both sides

\frac{992 k ^{6}}{992} = \frac{36}{992}

Divide the numbers

k^{6} = \frac{36}{992}

Cancel out the common factor 4

k^{6} = \frac{9}{248}

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

k = \pm 6 \frac{9}{248}

Simplify the expression

More Steps

Evaluate

6 \frac{9}{248}

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

\frac{6 9}{6 248}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{3 3}{6 248}

Multiply by the Conjugate

\frac{3 3 \times 6 24 8 ^{5}}{6 248 \times 6 24 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

33 \times 6 24 8^{5}

Use n a = mn a^{m} to expand the expression

6 3^{2} \times 6 24 8^{5}

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

6 3^{2} \times 24 8^{5}

Calculate the product

6 9 \times 24 8^{5}

\frac{6 9 \times 24 8 ^{5}}{6 248 \times 6 24 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

6248 \times 6 24 8^{5}

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

6 248 \times 24 8^{5}

Calculate the product

6 24 8^{6}

Reduce the index of the radical and exponent with 6

248

\frac{6 9 \times 24 8 ^{5}}{248}

k = \pm \frac{6 9 \times 24 8 ^{5}}{248}

Separate the equation into 2 possible cases

k = \frac{6 9 \times 24 8 ^{5}}{248} k = - \frac{6 9 \times 24 8 ^{5}}{248}

Solution

k_{1} = - \frac{6 9 \times 24 8 ^{5}}{248}, k_{2} = \frac{6 9 \times 24 8 ^{5}}{248}

Alternative Form

k_{1} \approx - 0.575394, k_{2} \approx 0.575394

Show Solution

K^6992 36

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression