Solve for x square root of 3x-1=2 square root of 5

$\sqrt{3 x - 1} = 2 \sqrt{5}$

Step 1

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

${\sqrt{3 x - 1}}^{2} = {(2 \sqrt{5})}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 1}$ as ${(3 x - 1)}^{\frac{1}{2}}$ .

${({(3 x - 1)}^{\frac{1}{2}})}^{2} = {(2 \sqrt{5})}^{2}$

Simplify the left side.

Simplify ${({(3 x - 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 1)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 1)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{5})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 1)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{5})}^{2}$

Rewrite the expression.

${(3 x - 1)}^{1} = {(2 \sqrt{5})}^{2}$

Simplify.

$3 x - 1 = {(2 \sqrt{5})}^{2}$

Simplify the right side.

Simplify ${(2 \sqrt{5})}^{2}$ .

Simplify the expression.

Apply the product rule to $2 \sqrt{5}$ .

$3 x - 1 = 2^{2} {\sqrt{5}}^{2}$

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

$3 x - 1 = 4 {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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

$3 x - 1 = 4 {(5^{\frac{1}{2}})}^{2}$

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

$3 x - 1 = 4 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$3 x - 1 = 4 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x - 1 = 4 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$3 x - 1 = 4 \cdot 5^{1}$

Evaluate the exponent.

$3 x - 1 = 4 \cdot 5$

Multiply $4$ by $5$ .

$3 x - 1 = 20$

Step 3

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$3 x = 20 + 1$

Add $20$ and $1$ .

$3 x = 21$

Divide each term in $3 x = 21$ by $3$ and simplify.

Divide each term in $3 x = 21$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3}$

Divide $x$ by $1$ .

$x = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$x = 7$

Solve for x square root of 3x-1=2 square root of 5

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