Pre-Algebra Examples

$224^{2} = \sqrt{2 (32) g}$

Step 1

Rewrite the equation as $\sqrt{2 (32) g} = 224^{2}$ .

$\sqrt{2 (32) g} = 224^{2}$

Step 2

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

${\sqrt{2 (32) g}}^{2} = {(224^{2})}^{2}$

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 $\sqrt{2 (32) g}$ as ${(2 (32) g)}^{\frac{1}{2}}$ .

${({(2 (32) g)}^{\frac{1}{2}})}^{2} = {(224^{2})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(2 (32) g)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(2 (32) g)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(2 (32) g)}^{\frac{1}{2} \cdot 2} = {(224^{2})}^{2}$

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.

${(2 (32) g)}^{\frac{1}{2} \cdot 2} = {(224^{2})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(2 (32) g)}^{1} = {(224^{2})}^{2}$

Step 3.2.1.2

Multiply $2$ by $32$ .

${(64 g)}^{1} = {(224^{2})}^{2}$

Step 3.2.1.3

Simplify.

$64 g = {(224^{2})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(224^{2})}^{2}$ .

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Step 3.3.1.1

Multiply the exponents in ${(224^{2})}^{2}$ .

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Step 3.3.1.1.1

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

$64 g = 224^{2 \cdot 2}$

Step 3.3.1.1.2

Multiply $2$ by $2$ .

$64 g = 224^{4}$

Step 3.3.1.2

Raise $224$ to the power of $4$ .

$64 g = 2517630976$

Step 4

Divide each term in $64 g = 2517630976$ by $64$ and simplify.

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Step 4.1

Divide each term in $64 g = 2517630976$ by $64$ .

$\frac{64 g}{64} = \frac{2517630976}{64}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $64$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{64 g}{64} = \frac{2517630976}{64}$

Step 4.2.1.2

Divide $g$ by $1$ .

$g = \frac{2517630976}{64}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $2517630976$ by $64$ .

$g = 39337984$