Solve 275-30 r^24

Question

Simplify the expression

275 - 120 r^{2}

Evaluate

275 - 30 r^{2} \times 4

Solution

275 - 120 r^{2}

Show Solution

5 (55 - 24 r^{2})

Evaluate

275 - 30 r^{2} \times 4

Multiply the terms

275 - 120 r^{2}

Solution

5 (55 - 24 r^{2})

Show Solution

r_{1} = - \frac{330}{12}, r_{2} = \frac{330}{12}

Alternative Form

r_{1} \approx - 1.513825, r_{2} \approx 1.513825

Evaluate

275 - 30 r^{2} \times 4

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

275 - 30 r^{2} \times 4 = 0

Multiply the terms

275 - 120 r^{2} = 0

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

- 120 r^{2} = 0 - 275

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

- 120 r^{2} = - 275

Change the signs on both sides of the equation

120 r^{2} = 275

Divide both sides

\frac{120 r ^{2}}{120} = \frac{275}{120}

Divide the numbers

r^{2} = \frac{275}{120}

Cancel out the common factor 5

r^{2} = \frac{55}{24}

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

r = \pm \frac{55}{24}

Simplify the expression

More Steps

Evaluate

\frac{55}{24}

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

\frac{55}{24}

Simplify the radical expression

More Steps

Evaluate

24

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

4 \times 6

Write the number in exponential form with the base of 2

2^{2} \times 6

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

2^{2} \times 6

Reduce the index of the radical and exponent with 2

26

\frac{55}{2 6}

Multiply by the Conjugate

\frac{55 \times 6}{2 6 \times 6}

Multiply the numbers

More Steps

Evaluate

55 \times 6

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

55 \times 6

Calculate the product

330

\frac{330}{2 6 \times 6}

Multiply the numbers

More Steps

Evaluate

26 \times 6

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

2 \times 6

Multiply the terms

12

\frac{330}{12}

r = \pm \frac{330}{12}

Separate the equation into 2 possible cases

r = \frac{330}{12} r = - \frac{330}{12}

Solution

r_{1} = - \frac{330}{12}, r_{2} = \frac{330}{12}

Alternative Form

r_{1} \approx - 1.513825, r_{2} \approx 1.513825

Show Solution