Basic Math Examples

${(9)}^{\frac{1}{2}} + \sqrt{25} - 8 \div 2 + 3^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{1}{2}} + \sqrt{25} - 8 \div 2 + 3^{2}$

Step 1.2

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

$3^{2 (\frac{1}{2})} + \sqrt{25} - 8 \div 2 + 3^{2}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$3^{2 (\frac{1}{2})} + \sqrt{25} - 8 \div 2 + 3^{2}$

Step 1.3.2

Rewrite the expression.

$3^{1} + \sqrt{25} - 8 \div 2 + 3^{2}$

Step 1.4

Evaluate the exponent.

$3 + \sqrt{25} - 8 \div 2 + 3^{2}$

Step 1.5

Rewrite $25$ as $5^{2}$ .

$3 + \sqrt{5^{2}} - 8 \div 2 + 3^{2}$

Step 1.6

Pull terms out from under the radical, assuming positive real numbers.

$3 + 5 - 8 \div 2 + 3^{2}$

Step 1.7

Divide $8$ by $2$ .

$3 + 5 - 1 \cdot 4 + 3^{2}$

Step 1.8

Multiply $- 1$ by $4$ .

$3 + 5 - 4 + 3^{2}$

Step 1.9

Raise $3$ to the power of $2$ .

$3 + 5 - 4 + 9$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $3$ and $5$ .

$8 - 4 + 9$

Step 2.2

Subtract $4$ from $8$ .

$4 + 9$

Step 2.3

Add $4$ and $9$ .

$13$