Algebra Examples

$\sqrt{y} = 3 \sqrt{5}$

Step 1

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

${\sqrt{y}}^{2} = {(3 \sqrt{5})}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.1.2

Simplify.

$y = {(3 \sqrt{5})}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify ${(3 \sqrt{5})}^{2}$ .

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Step 2.3.1.1

Simplify the expression.

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Step 2.3.1.1.1

Apply the product rule to $3 \sqrt{5}$ .

$y = 3^{2} {\sqrt{5}}^{2}$

Step 2.3.1.1.2

Raise $3$ to the power of $2$ .

$y = 9 {\sqrt{5}}^{2}$

Step 2.3.1.2

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

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Step 2.3.1.2.1

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

$y = 9 {(5^{\frac{1}{2}})}^{2}$

Step 2.3.1.2.2

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

$y = 9 \cdot 5^{\frac{1}{2} \cdot 2}$

Step 2.3.1.2.3

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

$y = 9 \cdot 5^{\frac{2}{2}}$

Step 2.3.1.2.4

Cancel the common factor of $2$ .

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Step 2.3.1.2.4.1

Cancel the common factor.

$y = 9 \cdot 5^{\frac{2}{2}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$y = 9 \cdot 5^{1}$

Step 2.3.1.2.5

Evaluate the exponent.

$y = 9 \cdot 5$

Step 2.3.1.3

Multiply $9$ by $5$ .

$y = 45$