Solve 2024 m^2400-60

Question

Simplify the expression

809600 m^{2} - 60

Evaluate

2024 m^{2} \times 400 - 60

Solution

809600 m^{2} - 60

Show Solution

20 (40480 m^{2} - 3)

Evaluate

2024 m^{2} \times 400 - 60

Multiply the terms

809600 m^{2} - 60

Solution

20 (40480 m^{2} - 3)

Show Solution

m_{1} = - \frac{7590}{10120}, m_{2} = \frac{7590}{10120}

Alternative Form

m_{1} \approx - 0.008609, m_{2} \approx 0.008609

Evaluate

2024 m^{2} \times 400 - 60

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

2024 m^{2} \times 400 - 60 = 0

Multiply the terms

809600 m^{2} - 60 = 0

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

809600 m^{2} = 0 + 60

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

809600 m^{2} = 60

Divide both sides

\frac{809600 m ^{2}}{809600} = \frac{60}{809600}

Divide the numbers

m^{2} = \frac{60}{809600}

Cancel out the common factor 20

m^{2} = \frac{3}{40480}

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

m = \pm \frac{3}{40480}

Simplify the expression

More Steps

Evaluate

\frac{3}{40480}

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

\frac{3}{40480}

Simplify the radical expression

More Steps

Evaluate

40480

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

16 \times 2530

Write the number in exponential form with the base of 4

4^{2} \times 2530

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

4^{2} \times 2530

Reduce the index of the radical and exponent with 2

42530

\frac{3}{4 2530}

Multiply by the Conjugate

\frac{3 \times 2530}{4 2530 \times 2530}

Multiply the numbers

More Steps

Evaluate

3 \times 2530

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

3 \times 2530

Calculate the product

7590

\frac{7590}{4 2530 \times 2530}

Multiply the numbers

More Steps

Evaluate

42530 \times 2530

When a square root of an expression is multiplied by itself,the result is that expression

4 \times 2530

Multiply the terms

10120

\frac{7590}{10120}

m = \pm \frac{7590}{10120}

Separate the equation into 2 possible cases

m = \frac{7590}{10120} m = - \frac{7590}{10120}

Solution

m_{1} = - \frac{7590}{10120}, m_{2} = \frac{7590}{10120}

Alternative Form

m_{1} \approx - 0.008609, m_{2} \approx 0.008609

Show Solution