Math Snap

STEP 1

Assumptions1. We are given the expression $\left(5^{}+12^{}\right)^{\frac{1}{}}$
. We need to simplify this expression3. We will use the order of operations, which states that operations inside parentheses are performed first, followed by exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).

STEP 2

First, we need to calculate the squares of5 and12 inside the parentheses.
$$5^{2} =5 \times5$$$$12^{2} =12 \times12$$

STEP 3

Now, calculate the squares.
$$5^{2} =25$$$$12^{2} =144$$

STEP 4

Replace the squares in the original expression with their calculated values.
$$\left(^{2}+12^{2}\right)^{\frac{1}{2}} = \left(25+144\right)^{\frac{1}{2}}$$

STEP 5

Add the numbers inside the parentheses.
$$\left(25+144\right)^{\frac{1}{2}} =169^{\frac{1}{2}}$$

Now, we need to calculate the square root of169. The square root of a number is a value that, when multiplied by itself, gives the original number.
$$169^{\frac{1}{2}} =13$$So, the simplified form of the given expression $\left(5^{2}+12^{2}\right)^{\frac{1}{2}}$ is13.