Algebra Examples

3 \sqrt{4 a} = 42

$3 \sqrt{4 a} = 42$

Step 1

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

{(3 \sqrt{4 a})}^{2} = 42^{2}

${(3 \sqrt{4 a})}^{2} = 42^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{4 a}

$\sqrt{4 a}$ as

{(4 a)}^{\frac{1}{2}}

${(4 a)}^{\frac{1}{2}}$ .

{(3 {(4 a)}^{\frac{1}{2}})}^{2} = 42^{2}

${(3 {(4 a)}^{\frac{1}{2}})}^{2} = 42^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

{(3 {(4 a)}^{\frac{1}{2}})}^{2}

${(3 {(4 a)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Simplify the expression.

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Step 2.2.1.1.1

Apply the product rule to

4 a

$4 a$ .

{(3 (4^{\frac{1}{2}} a^{\frac{1}{2}}))}^{2} = 42^{2}

${(3 (4^{\frac{1}{2}} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Step 2.2.1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

{(3 ({(2^{2})}^{\frac{1}{2}} a^{\frac{1}{2}}))}^{2} = 42^{2}

${(3 ({(2^{2})}^{\frac{1}{2}} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Step 2.2.1.1.3

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

{(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}

${(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}$

{(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}

${(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Step 2.2.1.2

Cancel the common factor of

2

$2$ .

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Step 2.2.1.2.1

Cancel the common factor.

${(3 (2^{2 (\frac{1}{2})} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Step 2.2.1.2.2

Rewrite the expression.

${(3 (2^{1} a^{\frac{1}{2}}))}^{2} = 42^{2}$

Step 2.2.1.3

Evaluate the exponent.

${(3 (2 a^{\frac{1}{2}}))}^{2} = 42^{2}$

Step 2.2.1.4

Multiply

$2$ by

$3$ .

${(6 a^{\frac{1}{2}})}^{2} = 42^{2}$

Step 2.2.1.5

Apply the product rule to

$6 a^{\frac{1}{2}}$ .

$6^{2} {(a^{\frac{1}{2}})}^{2} = 42^{2}$

Step 2.2.1.6

Raise

$6$ to the power of

$2$ .

$36 {(a^{\frac{1}{2}})}^{2} = 42^{2}$

Step 2.2.1.7

Multiply the exponents in

${(a^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.7.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$36 a^{\frac{1}{2} \cdot 2} = 42^{2}$

Step 2.2.1.7.2

Cancel the common factor of

$2$ .

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Step 2.2.1.7.2.1

Cancel the common factor.

$36 a^{\frac{1}{2} \cdot 2} = 42^{2}$

Step 2.2.1.7.2.2

Rewrite the expression.

$36 a^{1} = 42^{2}$

Step 2.2.1.8

Simplify.

$36 a = 42^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise

$42$ to the power of

$2$ .

$36 a = 1764$

Step 3

Divide each term in

$36 a = 1764$ by

$36$ and simplify.

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Step 3.1

Divide each term in

$36 a = 1764$ by

$36$ .

$\frac{36 a}{36} = \frac{1764}{36}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$36$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{36 a}{36} = \frac{1764}{36}$

Step 3.2.1.2

Divide

$a$ by

$1$ .

$a = \frac{1764}{36}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide

$1764$ by

$36$ .

$a = 49$