Solve 5j^220j-25 - ScanMath

Question

Simplify the expression

100 j^{3} - 25

Evaluate

5 j^{2} \times 20 j - 25

Solution

More Steps

Evaluate

5 j^{2} \times 20 j

Multiply the terms

100 j^{2} \times j

Multiply the terms with the same base by adding their exponents

100 j^{2 + 1}

Add the numbers

100 j^{3}

100 j^{3} - 25

Show Solution

Factor the expression

25 (4 j^{3} - 1)

Evaluate

5 j^{2} \times 20 j - 25

Multiply

More Steps

Evaluate

5 j^{2} \times 20 j

Multiply the terms

100 j^{2} \times j

Multiply the terms with the same base by adding their exponents

100 j^{2 + 1}

Add the numbers

100 j^{3}

100 j^{3} - 25

Solution

25 (4 j^{3} - 1)

Show Solution

Find the roots

j = \frac{3 2}{2}

Alternative Form

j \approx 0.629961

Evaluate

5 j^{2} \times 20 j - 25

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

5 j^{2} \times 20 j - 25 = 0

Multiply

More Steps

Multiply the terms

5 j^{2} \times 20 j

Multiply the terms

100 j^{2} \times j

Multiply the terms with the same base by adding their exponents

100 j^{2 + 1}

Add the numbers

100 j^{3}

100 j^{3} - 25 = 0

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

100 j^{3} = 0 + 25

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

100 j^{3} = 25

Divide both sides

\frac{100 j ^{3}}{100} = \frac{25}{100}

Divide the numbers

j^{3} = \frac{25}{100}

Cancel out the common factor 25

j^{3} = \frac{1}{4}

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

3 j^{3} = 3 \frac{1}{4}

Calculate

j = 3 \frac{1}{4}

Solution

More Steps

Evaluate

3 \frac{1}{4}

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

\frac{3 1}{3 4}

Simplify the radical expression

\frac{1}{3 4}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

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

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

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

Simplify

\frac{1}{2}

\frac{3 2}{2}

j = \frac{3 2}{2}

Alternative Form

j \approx 0.629961

Show Solution