Basic Math Examples

$\sqrt{200 y^{2}} + \frac{4 y}{\sqrt{2}} + \frac{80}{49}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $200 y^{2}$ as ${(10 y)}^{2} \cdot 2$ .

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Step 1.1.1

Factor $100$ out of $200$ .

$\sqrt{100 (2) y^{2}} + \frac{4 y}{\sqrt{2}} + \frac{80}{49}$

Step 1.1.2

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2 y^{2}} + \frac{4 y}{\sqrt{2}} + \frac{80}{49}$

Step 1.1.3

Move $2$ .

$\sqrt{10^{2} y^{2} \cdot 2} + \frac{4 y}{\sqrt{2}} + \frac{80}{49}$

Step 1.1.4

Rewrite $10^{2} y^{2}$ as ${(10 y)}^{2}$ .

$\sqrt{{(10 y)}^{2} \cdot 2} + \frac{4 y}{\sqrt{2}} + \frac{80}{49}$

Step 1.2

Pull terms out from under the radical.

$10 y \sqrt{2} + \frac{4 y}{\sqrt{2}} + \frac{80}{49}$

Step 1.3

Multiply $\frac{4 y}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$10 y \sqrt{2} + \frac{4 y}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} + \frac{80}{49}$

Step 1.4

Combine and simplify the denominator.

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Step 1.4.1

Multiply $\frac{4 y}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{\sqrt{2} \sqrt{2}} + \frac{80}{49}$

Step 1.4.2

Raise $\sqrt{2}$ to the power of $1$ .

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} + \frac{80}{49}$

Step 1.4.3

Raise $\sqrt{2}$ to the power of $1$ .

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} + \frac{80}{49}$

Step 1.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{{\sqrt{2}}^{1 + 1}} + \frac{80}{49}$

Step 1.4.5

Add $1$ and $1$ .

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{{\sqrt{2}}^{2}} + \frac{80}{49}$

Step 1.4.6

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 1.4.6.1

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

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} + \frac{80}{49}$

Step 1.4.6.2

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

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{2^{\frac{1}{2} \cdot 2}} + \frac{80}{49}$

Step 1.4.6.3

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

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{2^{\frac{2}{2}}} + \frac{80}{49}$

Step 1.4.6.4

Cancel the common factor of $2$ .

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Step 1.4.6.4.1

Cancel the common factor.

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{2^{\frac{2}{2}}} + \frac{80}{49}$

Step 1.4.6.4.2

Rewrite the expression.

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{2^{1}} + \frac{80}{49}$

Step 1.4.6.5

Evaluate the exponent.

$10 y \sqrt{2} + \frac{4 y \sqrt{2}}{2} + \frac{80}{49}$

Step 1.5

Cancel the common factor of $4$ and $2$ .

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Step 1.5.1

Factor $2$ out of $4 y \sqrt{2}$ .

$10 y \sqrt{2} + \frac{2 (2 y \sqrt{2})}{2} + \frac{80}{49}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $2$ .

$10 y \sqrt{2} + \frac{2 (2 y \sqrt{2})}{2 (1)} + \frac{80}{49}$

Step 1.5.2.2

Cancel the common factor.

$10 y \sqrt{2} + \frac{2 (2 y \sqrt{2})}{2 \cdot 1} + \frac{80}{49}$

Step 1.5.2.3

Rewrite the expression.

$10 y \sqrt{2} + \frac{2 y \sqrt{2}}{1} + \frac{80}{49}$

Step 1.5.2.4

Divide $2 y \sqrt{2}$ by $1$ .

$10 y \sqrt{2} + 2 y \sqrt{2} + \frac{80}{49}$

Step 2

Add $10 y \sqrt{2}$ and $2 y \sqrt{2}$ .

$12 y \sqrt{2} + \frac{80}{49}$