Solve for j 5 square root of j=1

$5 \sqrt{j} = 1$

Step 1

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

${(5 \sqrt{j})}^{2} = 1^{2}$

Step 2

Simplify each side of the equation.

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

${(5 j^{\frac{1}{2}})}^{2} = 1^{2}$

Simplify the left side.

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

Apply the product rule to $5 j^{\frac{1}{2}}$ .

$5^{2} {(j^{\frac{1}{2}})}^{2} = 1^{2}$

Raise $5$ to the power of $2$ .

$25 {(j^{\frac{1}{2}})}^{2} = 1^{2}$

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

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

$25 j^{\frac{1}{2} \cdot 2} = 1^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 j^{\frac{1}{2} \cdot 2} = 1^{2}$

Rewrite the expression.

$25 j^{1} = 1^{2}$

Simplify.

$25 j = 1^{2}$

Simplify the right side.

One to any power is one.

$25 j = 1$

Step 3

Divide each term in $25 j = 1$ by $25$ and simplify.

Divide each term in $25 j = 1$ by $25$ .

$\frac{25 j}{25} = \frac{1}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 j}{25} = \frac{1}{25}$

Divide $j$ by $1$ .

$j = \frac{1}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$j = \frac{1}{25}$

Decimal Form:

$j = 0.04$