Solve r^2314-16 - ScanMath

Question

Simplify the expression

314 r^{2} - 16

Evaluate

r^{2} \times 314 - 16

Solution

314 r^{2} - 16

Show Solution

2 (157 r^{2} - 8)

Evaluate

r^{2} \times 314 - 16

Use the commutative property to reorder the terms

314 r^{2} - 16

Solution

2 (157 r^{2} - 8)

Show Solution

r_{1} = - \frac{2 314}{157}, r_{2} = \frac{2 314}{157}

Alternative Form

r_{1} \approx - 0.225733, r_{2} \approx 0.225733

Evaluate

r^{2} \times 314 - 16

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

r^{2} \times 314 - 16 = 0

Use the commutative property to reorder the terms

314 r^{2} - 16 = 0

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

314 r^{2} = 0 + 16

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

314 r^{2} = 16

Divide both sides

\frac{314 r ^{2}}{314} = \frac{16}{314}

Divide the numbers

r^{2} = \frac{16}{314}

Cancel out the common factor 2

r^{2} = \frac{8}{157}

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

r = \pm \frac{8}{157}

Simplify the expression

More Steps

Evaluate

\frac{8}{157}

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

\frac{8}{157}

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}{157}

Multiply by the Conjugate

\frac{2 2 \times 157}{157 \times 157}

Multiply the numbers

More Steps

Evaluate

2 \times 157

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

2 \times 157

Calculate the product

314

\frac{2 314}{157 \times 157}

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

\frac{2 314}{157}

r = \pm \frac{2 314}{157}

Separate the equation into 2 possible cases

r = \frac{2 314}{157} r = - \frac{2 314}{157}

Solution

r_{1} = - \frac{2 314}{157}, r_{2} = \frac{2 314}{157}

Alternative Form

r_{1} \approx - 0.225733, r_{2} \approx 0.225733

Show Solution