Solve for y y square root of y+1=0

$y \sqrt{y + 1} = 0$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${(y \sqrt{y + 1})}^{2} = 0^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y + 1}$ as ${(y + 1)}^{\frac{1}{2}}$ .

${(y {(y + 1)}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

Simplify ${(y {(y + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $y {(y + 1)}^{\frac{1}{2}}$ .

$y^{2} {({(y + 1)}^{\frac{1}{2}})}^{2} = 0^{2}$

Multiply the exponents in ${({(y + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{2} {(y + 1)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{2} {(y + 1)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

$y^{2} {(y + 1)}^{1} = 0^{2}$

Simplify.

$y^{2} (y + 1) = 0^{2}$

Apply the distributive property.

$y^{2} y + y^{2} \cdot 1 = 0^{2}$

Multiply $y^{2}$ by $y$ by adding the exponents.

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$y^{2} y^{1} + y^{2} \cdot 1 = 0^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y^{2 + 1} + y^{2} \cdot 1 = 0^{2}$

Add $2$ and $1$ .

$y^{3} + y^{2} \cdot 1 = 0^{2}$

Multiply $y^{2}$ by $1$ .

$y^{3} + y^{2} = 0^{2}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$y^{3} + y^{2} = 0$

Step 3

Solve for $y$ .

Factor $y^{2}$ out of $y^{3} + y^{2}$ .

Factor $y^{2}$ out of $y^{3}$ .

$y^{2} y + y^{2} = 0$

Multiply by $1$ .

$y^{2} y + y^{2} \cdot 1 = 0$

Factor $y^{2}$ out of $y^{2} y + y^{2} \cdot 1$ .

$y^{2} (y + 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y^{2} = 0$

$y + 1 = 0$

Set $y^{2}$ equal to $0$ and solve for $y$ .

Set $y^{2}$ equal to $0$ .

$y^{2} = 0$

Solve $y^{2} = 0$ for $y$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$y = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 0$

Plus or minus $0$ is $0$ .

$y = 0$

Set $y + 1$ equal to $0$ and solve for $y$ .

Set $y + 1$ equal to $0$ .

$y + 1 = 0$

Subtract $1$ from both sides of the equation.

$y = - 1$

The final solution is all the values that make $y^{2} (y + 1) = 0$ true.

$y = 0, - 1$

Solve for y y square root of y+1=0

Related Questions

Support LCMGCF.com by disabling your adblocker.