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

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

Step 1

Subtract $\sqrt{y}$ from both sides of the equation.

$\sqrt{x} = - \sqrt{y}$

Step 2

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

${\sqrt{x}}^{2} = {(- \sqrt{y})}^{2}$

Step 3

Simplify each side of the equation.

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

${(x^{\frac{1}{2}})}^{2} = {(- \sqrt{y})}^{2}$

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = {(- \sqrt{y})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(- \sqrt{y})}^{2}$

Rewrite the expression.

$x^{1} = {(- \sqrt{y})}^{2}$

Simplify.

$x = {(- \sqrt{y})}^{2}$

Simplify the right side.

Simplify ${(- \sqrt{y})}^{2}$ .

Simplify the expression.

Apply the product rule to $- \sqrt{y}$ .

$x = {(- 1)}^{2} {\sqrt{y}}^{2}$

Raise $- 1$ to the power of $2$ .

$x = 1 {\sqrt{y}}^{2}$

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

$x = {\sqrt{y}}^{2}$

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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

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

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

$x = y^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x = y^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = y^{\frac{2}{2}}$

Rewrite the expression.

$x = y^{1}$

Simplify.

$x = y$

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

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