Solve r^2421-8 - ScanMath

Question

Simplify the expression

421 r^{2} - 8

Evaluate

r^{2} \times 421 - 8

Solution

421 r^{2} - 8

Show Solution

r_{1} = - \frac{2 842}{421}, r_{2} = \frac{2 842}{421}

Alternative Form

r_{1} \approx - 0.137849, r_{2} \approx 0.137849

Evaluate

r^{2} \times 421 - 8

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

r^{2} \times 421 - 8 = 0

Use the commutative property to reorder the terms

421 r^{2} - 8 = 0

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

421 r^{2} = 0 + 8

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

421 r^{2} = 8

Divide both sides

\frac{421 r ^{2}}{421} = \frac{8}{421}

Divide the numbers

r^{2} = \frac{8}{421}

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

r = \pm \frac{8}{421}

Simplify the expression

More Steps

Evaluate

\frac{8}{421}

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

\frac{8}{421}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{2 2}{421}

Multiply by the Conjugate

\frac{2 2 \times 421}{421 \times 421}

Multiply the numbers

More Steps

Evaluate

2 \times 421

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

2 \times 421

Calculate the product

842

\frac{2 842}{421 \times 421}

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

\frac{2 842}{421}

r = \pm \frac{2 842}{421}

Separate the equation into 2 possible cases

r = \frac{2 842}{421} r = - \frac{2 842}{421}

Solution

r_{1} = - \frac{2 842}{421}, r_{2} = \frac{2 842}{421}

Alternative Form

r_{1} \approx - 0.137849, r_{2} \approx 0.137849

Show Solution