Basic Math Examples

$53 = \sqrt{15 y}$

Step 1

Rewrite the equation as $\sqrt{15 y} = 53$ .

$\sqrt{15 y} = 53$

Step 2

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

${\sqrt{15 y}}^{2} = 53^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 y}$ as ${(15 y)}^{\frac{1}{2}}$ .

${({(15 y)}^{\frac{1}{2}})}^{2} = 53^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(15 y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(15 y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(15 y)}^{\frac{1}{2} \cdot 2} = 53^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(15 y)}^{\frac{1}{2} \cdot 2} = 53^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(15 y)}^{1} = 53^{2}$

Step 3.2.1.2

Simplify.

$15 y = 53^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $53$ to the power of $2$ .

$15 y = 2809$

Step 4

Divide each term in $15 y = 2809$ by $15$ and simplify.

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Step 4.1

Divide each term in $15 y = 2809$ by $15$ .

$\frac{15 y}{15} = \frac{2809}{15}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $15$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{15 y}{15} = \frac{2809}{15}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{2809}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{2809}{15}$

Decimal Form:

$y = 187.2\overline{6}$

Mixed Number Form:

$y = 187 \frac{4}{15}$