Basic Math Examples

$- 4 + 3 \sqrt{30 - 10} + {(5^{0})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Subtract $10$ from $30$ .

$- 4 + 3 \sqrt{20} + {(5^{0})}^{2}$

Step 1.2

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.2.1

Factor $4$ out of $20$ .

$- 4 + 3 \sqrt{4 (5)} + {(5^{0})}^{2}$

Step 1.2.2

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

$- 4 + 3 \sqrt{2^{2} \cdot 5} + {(5^{0})}^{2}$

$- 4 + 3 \sqrt{2^{2} \cdot 5} + {(5^{0})}^{2}$

Step 1.3

Pull terms out from under the radical.

$- 4 + 3 (2 \sqrt{5}) + {(5^{0})}^{2}$

Step 1.4

Multiply $2$ by $3$ .

$- 4 + 6 \sqrt{5} + {(5^{0})}^{2}$

Step 1.5

Multiply the exponents in ${(5^{0})}^{2}$ .

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Step 1.5.1

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

$- 4 + 6 \sqrt{5} + 5^{0 \cdot 2}$

Step 1.5.2

Multiply $0$ by $2$ .

$- 4 + 6 \sqrt{5} + 5^{0}$

$- 4 + 6 \sqrt{5} + 5^{0}$

Step 1.6

Anything raised to $0$ is $1$ .

$- 4 + 6 \sqrt{5} + 1$

$- 4 + 6 \sqrt{5} + 1$

Step 2

Add $- 4$ and $1$ .

$- 3 + 6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 + 6 \sqrt{5}$

Decimal Form:

$10.41640786 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$