Basic Math Examples

$1.05 = \frac{\sqrt{y}}{2}$

Step 1

Rewrite the equation as $\frac{\sqrt{y}}{2} = 1.05$ .

$\frac{\sqrt{y}}{2} = 1.05$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{\sqrt{y}}{2} = 2 \cdot 1.05$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{\sqrt{y}}{2} = 2 \cdot 1.05$

Step 3.1.1.2

Rewrite the expression.

$\sqrt{y} = 2 \cdot 1.05$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $1.05$ .

$\sqrt{y} = 2.1$

Step 4

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

${\sqrt{y}}^{2} = {2.1}^{2}$

Step 5

Simplify each side of the equation.

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Step 5.1

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

${(y^{\frac{1}{2}})}^{2} = {2.1}^{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

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

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Step 5.2.1.1.1

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

$y^{\frac{1}{2} \cdot 2} = {2.1}^{2}$

Step 5.2.1.1.2

Cancel the common factor of $2$ .

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Step 5.2.1.1.2.1

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = {2.1}^{2}$

Step 5.2.1.1.2.2

Rewrite the expression.

$y^{1} = {2.1}^{2}$

Step 5.2.1.2

Simplify.

$y = {2.1}^{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Raise $2.1$ to the power of $2$ .

$y = 4.41$