Solve q^37:100-110

Question

Simplify the expression

\frac{7 q ^{3} - 11000}{100}

Evaluate

q^{3} \times 7 \div 100 - 110

Use the commutative property to reorder the terms

7 q^{3} \div 100 - 110

Rewrite the expression

\frac{7 q ^{3}}{100} - 110

Reduce fractions to a common denominator

\frac{7 q ^{3}}{100} - \frac{110 \times 100}{100}

Write all numerators above the common denominator

\frac{7 q ^{3} - 110 \times 100}{100}

Solution

\frac{7 q ^{3} - 11000}{100}

Show Solution

Find the roots

q = \frac{10 3 539}{7}

Alternative Form

q \approx 11.626033

Evaluate

q^{3} \times 7 \div 100 - 110

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

q^{3} \times 7 \div 100 - 110 = 0

Use the commutative property to reorder the terms

7 q^{3} \div 100 - 110 = 0

Rewrite the expression

\frac{7 q ^{3}}{100} - 110 = 0

Subtract the terms

More Steps

Simplify

\frac{7 q ^{3}}{100} - 110

Reduce fractions to a common denominator

\frac{7 q ^{3}}{100} - \frac{110 \times 100}{100}

Write all numerators above the common denominator

\frac{7 q ^{3} - 110 \times 100}{100}

Multiply the numbers

\frac{7 q ^{3} - 11000}{100}

\frac{7 q ^{3} - 11000}{100} = 0

Simplify

7 q^{3} - 11000 = 0

Move the constant to the right side

7 q^{3} = 11000

Divide both sides

\frac{7 q ^{3}}{7} = \frac{11000}{7}

Divide the numbers

q^{3} = \frac{11000}{7}

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

3 q^{3} = 3 \frac{11000}{7}

Calculate

q = 3 \frac{11000}{7}

Solution

More Steps

Evaluate

3 \frac{11000}{7}

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

\frac{3 11000}{3 7}

Simplify the radical expression

More Steps

Evaluate

311000

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

3 1000 \times 11

Write the number in exponential form with the base of 10

3 1 0^{3} \times 11

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

3 1 0^{3} \times 311

Reduce the index of the radical and exponent with 3

10311

\frac{10 3 11}{3 7}

Multiply by the Conjugate

\frac{10 3 11 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{10 3 11 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 349

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

3 11 \times 49

Calculate the product

3539

\frac{10 3 539}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{10 3 539}{7}

q = \frac{10 3 539}{7}

Alternative Form

q \approx 11.626033

Show Solution