Solve 62368-1f^2023

Question

Simplify the expression

62368 - 23 f^{2}

Evaluate

62368 - 1 \times f^{2} \times 23

Solution

More Steps

Evaluate

1 \times f^{2} \times 23

Rewrite the expression

f^{2} \times 23

Use the commutative property to reorder the terms

23 f^{2}

62368 - 23 f^{2}

Show Solution

f_{1} = - \frac{4 89654}{23}, f_{2} = \frac{4 89654}{23}

Alternative Form

f_{1} \approx - 52.073527, f_{2} \approx 52.073527

Evaluate

62368 - 1 \times f^{2} \times 23

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

62368 - 1 \times f^{2} \times 23 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times f^{2} \times 23

Rewrite the expression

f^{2} \times 23

Use the commutative property to reorder the terms

23 f^{2}

62368 - 23 f^{2} = 0

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

- 23 f^{2} = 0 - 62368

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

- 23 f^{2} = - 62368

Change the signs on both sides of the equation

23 f^{2} = 62368

Divide both sides

\frac{23 f ^{2}}{23} = \frac{62368}{23}

Divide the numbers

f^{2} = \frac{62368}{23}

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

f = \pm \frac{62368}{23}

Simplify the expression

More Steps

Evaluate

\frac{62368}{23}

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

\frac{62368}{23}

Simplify the radical expression

More Steps

Evaluate

62368

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

16 \times 3898

Write the number in exponential form with the base of 4

4^{2} \times 3898

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

4^{2} \times 3898

Reduce the index of the radical and exponent with 2

43898

\frac{4 3898}{23}

Multiply by the Conjugate

\frac{4 3898 \times 23}{23 \times 23}

Multiply the numbers

More Steps

Evaluate

3898 \times 23

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

3898 \times 23

Calculate the product

89654

\frac{4 89654}{23 \times 23}

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

\frac{4 89654}{23}

f = \pm \frac{4 89654}{23}

Separate the equation into 2 possible cases

f = \frac{4 89654}{23} f = - \frac{4 89654}{23}

Solution

f_{1} = - \frac{4 89654}{23}, f_{2} = \frac{4 89654}{23}

Alternative Form

f_{1} \approx - 52.073527, f_{2} \approx 52.073527

Show Solution