Solve 4y 155y-1 - ScanMath

Question

Simplify the expression

620 y^{2} - 1

Evaluate

4 y \times 155 y - 1

Solution

More Steps

Evaluate

4 y \times 155 y

Multiply the terms

620 y \times y

Multiply the terms

620 y^{2}

620 y^{2} - 1

Show Solution

y_{1} = - \frac{155}{310}, y_{2} = \frac{155}{310}

Alternative Form

y_{1} \approx - 0.040161, y_{2} \approx 0.040161

Evaluate

4 y \times 155 y - 1

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

4 y \times 155 y - 1 = 0

Multiply

More Steps

Multiply the terms

4 y \times 155 y

Multiply the terms

620 y \times y

Multiply the terms

620 y^{2}

620 y^{2} - 1 = 0

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

620 y^{2} = 0 + 1

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

620 y^{2} = 1

Divide both sides

\frac{620 y ^{2}}{620} = \frac{1}{620}

Divide the numbers

y^{2} = \frac{1}{620}

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

y = \pm \frac{1}{620}

Simplify the expression

More Steps

Evaluate

\frac{1}{620}

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

\frac{1}{620}

Simplify the radical expression

\frac{1}{620}

Simplify the radical expression

More Steps

Evaluate

620

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

4 \times 155

Write the number in exponential form with the base of 2

2^{2} \times 155

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

2^{2} \times 155

Reduce the index of the radical and exponent with 2

2155

\frac{1}{2 155}

Multiply by the Conjugate

\frac{155}{2 155 \times 155}

Multiply the numbers

More Steps

Evaluate

2155 \times 155

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

2 \times 155

Multiply the terms

310

\frac{155}{310}

y = \pm \frac{155}{310}

Separate the equation into 2 possible cases

y = \frac{155}{310} y = - \frac{155}{310}

Solution

y_{1} = - \frac{155}{310}, y_{2} = \frac{155}{310}

Alternative Form

y_{1} \approx - 0.040161, y_{2} \approx 0.040161

Show Solution