Solve for a square root of 5a+1+2=6

$\sqrt{5 a + 1} + 2 = 6$

Step 1

Move all terms not containing $\sqrt{5 a + 1}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\sqrt{5 a + 1} = 6 - 2$

Subtract $2$ from $6$ .

$\sqrt{5 a + 1} = 4$

Step 2

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

${\sqrt{5 a + 1}}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 a + 1}$ as ${(5 a + 1)}^{\frac{1}{2}}$ .

${({(5 a + 1)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(5 a + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 a + 1)}^{\frac{1}{2}})}^{2}$ .

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

${(5 a + 1)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 a + 1)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(5 a + 1)}^{1} = 4^{2}$

Simplify.

$5 a + 1 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$5 a + 1 = 16$

Step 4

Solve for $a$ .

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

Subtract $1$ from both sides of the equation.

$5 a = 16 - 1$

Subtract $1$ from $16$ .

$5 a = 15$

Divide each term in $5 a = 15$ by $5$ and simplify.

Divide each term in $5 a = 15$ by $5$ .

$\frac{5 a}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 a}{5} = \frac{15}{5}$

Divide $a$ by $1$ .

$a = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$a = 3$

Solve for a square root of 5a+1+2=6

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