Solve r1r11-221 - ScanMath

Question

Simplify the expression

11 r^{2} - 221

Evaluate

r \times 1 \times r \times 11 - 221

Solution

More Steps

Evaluate

r \times 1 \times r \times 11

Rewrite the expression

r \times r \times 11

Multiply the terms

r^{2} \times 11

Use the commutative property to reorder the terms

11 r^{2}

11 r^{2} - 221

Show Solution

r_{1} = - \frac{2431}{11}, r_{2} = \frac{2431}{11}

Alternative Form

r_{1} \approx - 4.482288, r_{2} \approx 4.482288

Evaluate

r \times 1 \times r \times 11 - 221

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

r \times 1 \times r \times 11 - 221 = 0

Multiply the terms

More Steps

Multiply the terms

r \times 1 \times r \times 11

Rewrite the expression

r \times r \times 11

Multiply the terms

r^{2} \times 11

Use the commutative property to reorder the terms

11 r^{2}

11 r^{2} - 221 = 0

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

11 r^{2} = 0 + 221

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

11 r^{2} = 221

Divide both sides

\frac{11 r ^{2}}{11} = \frac{221}{11}

Divide the numbers

r^{2} = \frac{221}{11}

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

r = \pm \frac{221}{11}

Simplify the expression

More Steps

Evaluate

\frac{221}{11}

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

\frac{221}{11}

Multiply by the Conjugate

\frac{221 \times 11}{11 \times 11}

Multiply the numbers

More Steps

Evaluate

221 \times 11

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

221 \times 11

Calculate the product

2431

\frac{2431}{11 \times 11}

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

\frac{2431}{11}

r = \pm \frac{2431}{11}

Separate the equation into 2 possible cases

r = \frac{2431}{11} r = - \frac{2431}{11}

Solution

r_{1} = - \frac{2431}{11}, r_{2} = \frac{2431}{11}

Alternative Form

r_{1} \approx - 4.482288, r_{2} \approx 4.482288

Show Solution