Basic Math Examples

$0.45 = 2 p \sqrt{l \div 9.8}$

Step 1

Rewrite the equation as $2 p \sqrt{l \div 9.8} = 0.45$ .

$2 p \sqrt{l \div 9.8} = 0.45$

Step 2

Divide each term in $2 p \sqrt{l \div 9.8} = 0.45$ by $2 p$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $2 p \sqrt{l \div 9.8} = 0.45$ by $2 p$ .

$\frac{2 p \sqrt{l \div 9.8}}{2 p} = \frac{0.45}{2 p}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{2 p \sqrt{l \div 9.8}}{2 p} = \frac{0.45}{2 p}$

Step 2.2.1.2

Rewrite the expression.

$\frac{p \sqrt{l \div 9.8}}{p} = \frac{0.45}{2 p}$

Step 2.2.2

Cancel the common factor of $p$ .

Tap for more steps...

Step 2.2.2.1

Cancel the common factor.

$\frac{p \sqrt{l \div 9.8}}{p} = \frac{0.45}{2 p}$

Step 2.2.2.2

Divide $\sqrt{l \div 9.8}$ by $1$ .

$\sqrt{l \div 9.8} = \frac{0.45}{2 p}$

Step 2.2.3

Rewrite the division as a fraction.

$\sqrt{\frac{l}{9.8}} = \frac{0.45}{2 p}$

Step 2.2.4

Multiply by $1$ .

$\sqrt{\frac{1 l}{9.8}} = \frac{0.45}{2 p}$

Step 2.2.5

Factor $9.8$ out of $9.8$ .

$\sqrt{\frac{1 l}{9.8 (1)}} = \frac{0.45}{2 p}$

Step 2.2.6

Separate fractions.

$\sqrt{\frac{1}{9.8} \cdot \frac{l}{1}} = \frac{0.45}{2 p}$

Step 2.2.7

Divide $1$ by $9.8$ .

$\sqrt{0.10204081 \frac{l}{1}} = \frac{0.45}{2 p}$

Step 2.2.8

Divide $l$ by $1$ .

$\sqrt{0.10204081 l} = \frac{0.45}{2 p}$

Step 2.2.9

Rewrite $0.10204081 l$ as ${({0.56518871}^{2})}^{2} l$ .

Tap for more steps...

Step 2.2.9.1

Rewrite $0.10204081$ as ${0.31943828}^{2}$ .

$\sqrt{{0.31943828}^{2} l} = \frac{0.45}{2 p}$

Step 2.2.9.2

Rewrite $0.31943828$ as ${0.56518871}^{2}$ .

$\sqrt{{({0.56518871}^{2})}^{2} l} = \frac{0.45}{2 p}$

Step 2.2.10

Pull terms out from under the radical.

${0.56518871}^{2} \sqrt{l} = \frac{0.45}{2 p}$

Step 2.2.11

Raise $0.56518871$ to the power of $2$ .

$0.31943828 \sqrt{l} = \frac{0.45}{2 p}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Factor $0.45$ out of $0.45$ .

$0.31943828 \sqrt{l} = \frac{0.45 (1)}{2 p}$

Step 2.3.2

Factor $2$ out of $2 p$ .

$0.31943828 \sqrt{l} = \frac{0.45 (1)}{2 (p)}$

Step 2.3.3

Separate fractions.

$0.31943828 \sqrt{l} = \frac{0.45}{2} \cdot \frac{1}{p}$

Step 2.3.4

Divide $0.45$ by $2$ .

$0.31943828 \sqrt{l} = 0.225 \frac{1}{p}$

Step 2.3.5

Combine $0.225$ and $\frac{1}{p}$ .

$0.31943828 \sqrt{l} = \frac{0.225}{p}$

Step 3

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

${(0.31943828 \sqrt{l})}^{2} = {(\frac{0.225}{p})}^{2}$

Step 4

Simplify each side of the equation.

Tap for more steps...

Step 4.1

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

${(0.31943828 l^{\frac{1}{2}})}^{2} = {(\frac{0.225}{p})}^{2}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify ${(0.31943828 l^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 4.2.1.1

Apply the product rule to $0.31943828 l^{\frac{1}{2}}$ .

${0.31943828}^{2} {(l^{\frac{1}{2}})}^{2} = {(\frac{0.225}{p})}^{2}$

Step 4.2.1.2

Raise $0.31943828$ to the power of $2$ .

$0.10204081 {(l^{\frac{1}{2}})}^{2} = {(\frac{0.225}{p})}^{2}$

Step 4.2.1.3

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

Tap for more steps...

Step 4.2.1.3.1

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

$0.10204081 l^{\frac{1}{2} \cdot 2} = {(\frac{0.225}{p})}^{2}$

Step 4.2.1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.3.2.1

Cancel the common factor.

$0.10204081 l^{\frac{1}{2} \cdot 2} = {(\frac{0.225}{p})}^{2}$

Step 4.2.1.3.2.2

Rewrite the expression.

$0.10204081 l^{1} = {(\frac{0.225}{p})}^{2}$

Step 4.2.1.4

Simplify.

$0.10204081 l = {(\frac{0.225}{p})}^{2}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Simplify ${(\frac{0.225}{p})}^{2}$ .

Tap for more steps...

Step 4.3.1.1

Apply the product rule to $\frac{0.225}{p}$ .

$0.10204081 l = \frac{{0.225}^{2}}{p^{2}}$

Step 4.3.1.2

Raise $0.225$ to the power of $2$ .

$0.10204081 l = \frac{0.050625}{p^{2}}$

Step 5

Divide each term in $0.10204081 l = \frac{0.050625}{p^{2}}$ by $0.10204081$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $0.10204081 l = \frac{0.050625}{p^{2}}$ by $0.10204081$ .

$\frac{0.10204081 l}{0.10204081} = \frac{\frac{0.050625}{p^{2}}}{0.10204081}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $0.10204081$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{0.10204081 l}{0.10204081} = \frac{\frac{0.050625}{p^{2}}}{0.10204081}$

Step 5.2.1.2

Divide $l$ by $1$ .

$l = \frac{\frac{0.050625}{p^{2}}}{0.10204081}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$l = \frac{0.050625}{p^{2}} \cdot \frac{1}{0.10204081}$

Step 5.3.2

Combine.

$l = \frac{0.050625 \cdot 1}{p^{2} \cdot 0.10204081}$

Step 5.3.3

Simplify the expression.

Tap for more steps...

Step 5.3.3.1

Multiply $0.050625$ by $1$ .

$l = \frac{0.050625}{p^{2} \cdot 0.10204081}$

Step 5.3.3.2

Move $0.10204081$ to the left of $p^{2}$ .

$l = \frac{0.050625}{0.10204081 \cdot p^{2}}$

Step 5.3.4

Factor $0.050625$ out of $0.050625$ .

$l = \frac{0.050625 (1)}{0.10204081 \cdot p^{2}}$

Step 5.3.5

Factor $0.10204081$ out of $0.10204081 \cdot p^{2}$ .

$l = \frac{0.050625 (1)}{0.10204081 (p^{2})}$

Step 5.3.6

Separate fractions.

$l = \frac{0.050625}{0.10204081} \cdot \frac{1}{p^{2}}$

Step 5.3.7

Divide $0.050625$ by $0.10204081$ .

$l = 0.496125 \frac{1}{p^{2}}$

Step 5.3.8

Combine $0.496125$ and $\frac{1}{p^{2}}$ .

$l = \frac{0.496125}{p^{2}}$