Evaluate square root of a^2+b^2=a+b

$\sqrt{a^{2} + b^{2}} = a + b$

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

${\sqrt{a^{2} + b^{2}}}^{2} = {(a + b)}^{2}$

Simplify each side of the equation.

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

${({(a^{2} + b^{2})}^{\frac{1}{2}})}^{2} = {(a + b)}^{2}$

Simplify the left side.

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

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

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

${(a^{2} + b^{2})}^{\frac{1}{2} \cdot 2} = {(a + b)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(a^{2} + b^{2})}^{\frac{1}{2} \cdot 2} = {(a + b)}^{2}$

Rewrite the expression.

${(a^{2} + b^{2})}^{1} = {(a + b)}^{2}$

Simplify.

$a^{2} + b^{2} = {(a + b)}^{2}$

Simplify the right side.

Simplify ${(a + b)}^{2}$ .

Rewrite ${(a + b)}^{2}$ as $(a + b) (a + b)$ .

$a^{2} + b^{2} = (a + b) (a + b)$

Expand $(a + b) (a + b)$ using the FOIL Method.

Apply the distributive property.

$a^{2} + b^{2} = a (a + b) + b (a + b)$

Apply the distributive property.

$a^{2} + b^{2} = a \cdot a + a b + b (a + b)$

Apply the distributive property.

$a^{2} + b^{2} = a \cdot a + a b + b a + b \cdot b$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$a^{2} + b^{2} = a^{2} + a b + b a + b \cdot b$

Multiply $b$ by $b$ .

$a^{2} + b^{2} = a^{2} + a b + b a + b^{2}$

Add $a b$ and $b a$ .

Reorder $b$ and $a$ .

$a^{2} + b^{2} = a^{2} + a b + a b + b^{2}$

Add $a b$ and $a b$ .

$a^{2} + b^{2} = a^{2} + 2 a b + b^{2}$

Solve for $a$ .

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$a^{2} + 2 a b + b^{2} = a^{2} + b^{2}$

Move all terms containing $a$ to the left side of the equation.

Subtract $a^{2}$ from both sides of the equation.

$a^{2} + 2 a b + b^{2} - a^{2} = b^{2}$

Combine the opposite terms in $a^{2} + 2 a b + b^{2} - a^{2}$ .

Subtract $a^{2}$ from $a^{2}$ .

$2 a b + b^{2} + 0 = b^{2}$

Add $2 a b + b^{2}$ and $0$ .

$2 a b + b^{2} = b^{2}$

Move all terms not containing $a$ to the right side of the equation.

Subtract $b^{2}$ from both sides of the equation.

$2 a b = b^{2} - b^{2}$

Subtract $b^{2}$ from $b^{2}$ .

$2 a b = 0$

Divide each term in $2 a b = 0$ by $2 b$ and simplify.

Divide each term in $2 a b = 0$ by $2 b$ .

$\frac{2 a b}{2 b} = \frac{0}{2 b}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a b}{2 b} = \frac{0}{2 b}$

Rewrite the expression.

$\frac{a b}{b} = \frac{0}{2 b}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{a b}{b} = \frac{0}{2 b}$

Divide $a$ by $1$ .

$a = \frac{0}{2 b}$

Simplify the right side.

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $0$ .

$a = \frac{2 (0)}{2 b}$

Cancel the common factors.

Factor $2$ out of $2 b$ .

$a = \frac{2 (0)}{2 (b)}$

Cancel the common factor.

$a = \frac{2 \cdot 0}{2 b}$

Rewrite the expression.

$a = \frac{0}{b}$

Divide $0$ by $b$ .

$a = 0$

Evaluate square root of a^2+b^2=a+b

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