Basic Math Examples

$0.5 = 2 p \sqrt{4 \div y}$

Step 1

Rewrite the equation as $2 p \sqrt{4 \div y} = 0.5$ .

$2 p \sqrt{4 \div y} = 0.5$

Step 2

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

${(2 p \sqrt{4 \div y})}^{2} = {0.5}^{2}$

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 $\sqrt{4 \div y}$ as ${(4 \div y)}^{\frac{1}{2}}$ .

${(2 p {(4 \div y)}^{\frac{1}{2}})}^{2} = {0.5}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(2 p {(4 \div y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Rewrite the division as a fraction.

${(2 p {(\frac{4}{y})}^{\frac{1}{2}})}^{2} = {0.5}^{2}$

Step 3.2.1.2

Apply the product rule to $\frac{4}{y}$ .

${(2 p \frac{4^{\frac{1}{2}}}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.3

Simplify the numerator.

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Step 3.2.1.3.1

Rewrite $4$ as $2^{2}$ .

${(2 p \frac{{(2^{2})}^{\frac{1}{2}}}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.3.2

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

${(2 p \frac{2^{2 (\frac{1}{2})}}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.3.3

Cancel the common factor of $2$ .

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Step 3.2.1.3.3.1

Cancel the common factor.

${(2 p \frac{2^{2 (\frac{1}{2})}}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.3.3.2

Rewrite the expression.

${(2 p \frac{2^{1}}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.3.4

Evaluate the exponent.

${(2 p \frac{2}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.4

Multiply $2 p \frac{2}{y^{\frac{1}{2}}}$ .

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Step 3.2.1.4.1

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

${(p \frac{2 \cdot 2}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.4.2

Multiply $2$ by $2$ .

${(p \frac{4}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.4.3

Combine $p$ and $\frac{4}{y^{\frac{1}{2}}}$ .

${(\frac{p \cdot 4}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.5

Move $4$ to the left of $p$ .

${(\frac{4 \cdot p}{y^{\frac{1}{2}}})}^{2} = {0.5}^{2}$

Step 3.2.1.6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.2.1.6.1

Apply the product rule to $\frac{4 p}{y^{\frac{1}{2}}}$ .

$\frac{{(4 p)}^{2}}{{(y^{\frac{1}{2}})}^{2}} = {0.5}^{2}$

Step 3.2.1.6.2

Apply the product rule to $4 p$ .

$\frac{4^{2} p^{2}}{{(y^{\frac{1}{2}})}^{2}} = {0.5}^{2}$

Step 3.2.1.7

Raise $4$ to the power of $2$ .

$\frac{16 p^{2}}{{(y^{\frac{1}{2}})}^{2}} = {0.5}^{2}$

Step 3.2.1.8

Simplify the denominator.

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Step 3.2.1.8.1

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

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Step 3.2.1.8.1.1

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

$\frac{16 p^{2}}{y^{\frac{1}{2} \cdot 2}} = {0.5}^{2}$

Step 3.2.1.8.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.8.1.2.1

Cancel the common factor.

$\frac{16 p^{2}}{y^{\frac{1}{2} \cdot 2}} = {0.5}^{2}$

Step 3.2.1.8.1.2.2

Rewrite the expression.

$\frac{16 p^{2}}{y^{1}} = {0.5}^{2}$

Step 3.2.1.8.2

Simplify.

$\frac{16 p^{2}}{y} = {0.5}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $0.5$ to the power of $2$ .

$\frac{16 p^{2}}{y} = 0.25$

Step 4

Solve for $y$ .

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Step 4.1

Find the LCD of the terms in the equation.

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Step 4.1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y, 1$

Step 4.1.2

The LCM of one and any expression is the expression.

$y$

Step 4.2

Multiply each term in $\frac{16 p^{2}}{y} = 0.25$ by $y$ to eliminate the fractions.

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Step 4.2.1

Multiply each term in $\frac{16 p^{2}}{y} = 0.25$ by $y$ .

$\frac{16 p^{2}}{y} y = 0.25 y$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $y$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{16 p^{2}}{y} y = 0.25 y$

Step 4.2.2.1.2

Rewrite the expression.

$16 p^{2} = 0.25 y$

Step 4.3

Solve the equation.

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Step 4.3.1

Rewrite the equation as $0.25 y = 16 p^{2}$ .

$0.25 y = 16 p^{2}$

Step 4.3.2

Divide each term in $0.25 y = 16 p^{2}$ by $0.25$ and simplify.

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Step 4.3.2.1

Divide each term in $0.25 y = 16 p^{2}$ by $0.25$ .

$\frac{0.25 y}{0.25} = \frac{16 p^{2}}{0.25}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

Cancel the common factor of $0.25$ .

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{0.25 y}{0.25} = \frac{16 p^{2}}{0.25}$

Step 4.3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{16 p^{2}}{0.25}$

Step 4.3.2.3

Simplify the right side.

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Step 4.3.2.3.1

Factor $16$ out of $16 p^{2}$ .

$y = \frac{16 (p^{2})}{0.25}$

Step 4.3.2.3.2

Factor $0.25$ out of $0.25$ .

$y = \frac{16 (p^{2})}{0.25 (1)}$

Step 4.3.2.3.3

Separate fractions.

$y = \frac{16}{0.25} \cdot \frac{p^{2}}{1}$

Step 4.3.2.3.4

Divide $16$ by $0.25$ .

$y = 64 \frac{p^{2}}{1}$

Step 4.3.2.3.5

Divide $p^{2}$ by $1$ .

$y = 64 p^{2}$