Solve w^224w-25 - ScanMath

Question

Simplify the expression

24 w^{3} - 25

Evaluate

w^{2} \times 24 w - 25

Solution

More Steps

Evaluate

w^{2} \times 24 w

Multiply the terms with the same base by adding their exponents

w^{2 + 1} \times 24

Add the numbers

w^{3} \times 24

Use the commutative property to reorder the terms

24 w^{3}

24 w^{3} - 25

Show Solution

w = \frac{3 225}{6}

Alternative Form

w \approx 1.0137

Evaluate

w^{2} \times 24 w - 25

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

w^{2} \times 24 w - 25 = 0

Multiply

More Steps

Multiply the terms

w^{2} \times 24 w

Multiply the terms with the same base by adding their exponents

w^{2 + 1} \times 24

Add the numbers

w^{3} \times 24

Use the commutative property to reorder the terms

24 w^{3}

24 w^{3} - 25 = 0

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

24 w^{3} = 0 + 25

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

24 w^{3} = 25

Divide both sides

\frac{24 w ^{3}}{24} = \frac{25}{24}

Divide the numbers

w^{3} = \frac{25}{24}

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

3 w^{3} = 3 \frac{25}{24}

Calculate

w = 3 \frac{25}{24}

Solution

More Steps

Evaluate

3 \frac{25}{24}

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

\frac{3 25}{3 24}

Simplify the radical expression

More Steps

Evaluate

324

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

3 8 \times 3

Write the number in exponential form with the base of 2

3 2^{3} \times 3

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

3 2^{3} \times 33

Reduce the index of the radical and exponent with 3

233

\frac{3 25}{2 3 3}

Multiply by the Conjugate

\frac{3 25 \times 3 3 ^{2}}{2 3 3 \times 3 3 ^{2}}

Simplify

\frac{3 25 \times 3 9}{2 3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

325 \times 39

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

3 25 \times 9

Calculate the product

3225

\frac{3 225}{2 3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

233 \times 3 3^{2}

Multiply the terms

2 \times 3

Multiply the terms

6

\frac{3 225}{6}

w = \frac{3 225}{6}

Alternative Form

w \approx 1.0137

Show Solution