Solve by Factoring 3 square root of x=27

$3 \sqrt{x} = 27$

Step 1

Subtract $27$ from both sides of the equation.

$3 \sqrt{x} - 27 = 0$

Step 2

Factor $3$ out of $3 \sqrt{x} - 27$ .

Factor $3$ out of $3 \sqrt{x}$ .

$3 (\sqrt{x}) - 27 = 0$

Factor $3$ out of $- 27$ .

$3 \sqrt{x} + 3 \cdot - 9 = 0$

Factor $3$ out of $3 \sqrt{x} + 3 \cdot - 9$ .

$3 (\sqrt{x} - 9) = 0$

Step 3

Divide each term in $3 (\sqrt{x} - 9) = 0$ by $3$ and simplify.

Divide each term in $3 (\sqrt{x} - 9) = 0$ by $3$ .

$\frac{3 (\sqrt{x} - 9)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (\sqrt{x} - 9)}{3} = \frac{0}{3}$

Divide $\sqrt{x} - 9$ by $1$ .

$\sqrt{x} - 9 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$\sqrt{x} - 9 = 0$

Step 4

Add $9$ to both sides of the equation.

$\sqrt{x} = 9$

Step 5

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

${\sqrt{x}}^{2} = 9^{2}$

Step 6

Simplify each side of the equation.

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

${(x^{\frac{1}{2}})}^{2} = 9^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

$x^{1} = 9^{2}$

Simplify.

$x = 9^{2}$

Simplify the right side.

Raise $9$ to the power of $2$ .

$x = 81$

Solve by Factoring 3 square root of x=27

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