Basic Math Examples

$\sqrt{3 b} = 3 \sqrt{2 b + 5}$

Step 1

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

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

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 $\sqrt{3 b}$ as ${(3 b)}^{\frac{1}{2}}$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

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

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.

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.1.2

Simplify.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

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

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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 $3 \sqrt{2 b + 5}$ .

$3 b = 3^{2} {\sqrt{2 b + 5}}^{2}$

Step 2.3.1.1.2

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

$3 b = 9 {\sqrt{2 b + 5}}^{2}$

Step 2.3.1.2

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

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Step 2.3.1.2.1

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

$3 b = 9 {({(2 b + 5)}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2.2

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

$3 b = 9 {(2 b + 5)}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.2.3

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

$3 b = 9 {(2 b + 5)}^{\frac{2}{2}}$

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.

$3 b = 9 {(2 b + 5)}^{\frac{2}{2}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$3 b = 9 {(2 b + 5)}^{1}$

Step 2.3.1.2.5

Simplify.

$3 b = 9 (2 b + 5)$

Step 2.3.1.3

Apply the distributive property.

$3 b = 9 (2 b) + 9 \cdot 5$

Step 2.3.1.4

Multiply.

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Step 2.3.1.4.1

Multiply $2$ by $9$ .

$3 b = 18 b + 9 \cdot 5$

Step 2.3.1.4.2

Multiply $9$ by $5$ .

$3 b = 18 b + 45$

Step 3

Solve for $b$ .

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Step 3.1

Move all terms containing $b$ to the left side of the equation.

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Step 3.1.1

Subtract $18 b$ from both sides of the equation.

$3 b - 18 b = 45$

Step 3.1.2

Subtract $18 b$ from $3 b$ .

$- 15 b = 45$

Step 3.2

Divide each term in $- 15 b = 45$ by $- 15$ and simplify.

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Step 3.2.1

Divide each term in $- 15 b = 45$ by $- 15$ .

$\frac{- 15 b}{- 15} = \frac{45}{- 15}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 15$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 15 b}{- 15} = \frac{45}{- 15}$

Step 3.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{45}{- 15}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $45$ by $- 15$ .

$b = - 3$

Step 4

Exclude the solutions that do not make $\sqrt{3 b} = 3 \sqrt{2 b + 5}$ true.

$No solution$