Sure, let's work through the problem step-by-step.
You are given the expression [tex]\( 3 \frac{1}{3} \times \sqrt{52} \)[/tex].
Step 1: Convert the mixed number to an improper fraction
First, we need to convert the mixed number [tex]\( 3 \frac{1}{3} \)[/tex] into an improper fraction. A mixed number consists of a whole number and a fraction. In this case, the whole number is 3, and the fraction is [tex]\(\frac{1}{3}\)[/tex].
To convert [tex]\( 3 \frac{1}{3} \)[/tex] into an improper fraction, multiply the whole number part (3) by the denominator of the fraction (3), then add the numerator of the fraction (1):
[tex]\[ 3 \cdot 3 + 1 = 9 + 1 = 10 \][/tex]
So, [tex]\( 3 \frac{1}{3} \)[/tex] can be written as [tex]\(\frac{10}{3}\)[/tex].
Now, if we express that fraction in decimal form, it becomes [tex]\( 3.3333333333333335 \)[/tex].
Step 2: Approximate the square root of 52
Next, we need to find the square root of 52. Using a calculator or other mathematical tool, we get:
[tex]\[ \sqrt{52} \approx 7.211102550927978 \][/tex]
Step 3: Multiply the two values
With the converted mixed number and the square root value in hand, the next step is to multiply them together:
[tex]\[ 3.3333333333333335 \times 7.211102550927978 \approx 24.03700850309326 \][/tex]
Thus, the result of [tex]\( 3 \frac{1}{3} \times \sqrt{52} \)[/tex] is approximately 24.03700850309326.
