Solve 48804-v^2010

Question

Simplify the expression

48804 - 10 v^{2}

Evaluate

48804 - v^{2} \times 10

Solution

48804 - 10 v^{2}

Show Solution

2 (24402 - 5 v^{2})

Evaluate

48804 - v^{2} \times 10

Use the commutative property to reorder the terms

48804 - 10 v^{2}

Solution

2 (24402 - 5 v^{2})

Show Solution

v_{1} = - \frac{7 2490}{5}, v_{2} = \frac{7 2490}{5}

Alternative Form

v_{1} \approx - 69.85986, v_{2} \approx 69.85986

Evaluate

48804 - v^{2} \times 10

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

48804 - v^{2} \times 10 = 0

Use the commutative property to reorder the terms

48804 - 10 v^{2} = 0

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

- 10 v^{2} = 0 - 48804

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

- 10 v^{2} = - 48804

Change the signs on both sides of the equation

10 v^{2} = 48804

Divide both sides

\frac{10 v ^{2}}{10} = \frac{48804}{10}

Divide the numbers

v^{2} = \frac{48804}{10}

Cancel out the common factor 2

v^{2} = \frac{24402}{5}

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

v = \pm \frac{24402}{5}

Simplify the expression

More Steps

Evaluate

\frac{24402}{5}

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

\frac{24402}{5}

Simplify the radical expression

More Steps

Evaluate

24402

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

49 \times 498

Write the number in exponential form with the base of 7

7^{2} \times 498

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

7^{2} \times 498

Reduce the index of the radical and exponent with 2

7498

\frac{7 498}{5}

Multiply by the Conjugate

\frac{7 498 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

498 \times 5

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

498 \times 5

Calculate the product

2490

\frac{7 2490}{5 \times 5}

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

\frac{7 2490}{5}

v = \pm \frac{7 2490}{5}

Separate the equation into 2 possible cases

v = \frac{7 2490}{5} v = - \frac{7 2490}{5}

Solution

v_{1} = - \frac{7 2490}{5}, v_{2} = \frac{7 2490}{5}

Alternative Form

v_{1} \approx - 69.85986, v_{2} \approx 69.85986

Show Solution