Sure, let's solve 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. The mixed number can be represented as the sum of the integer part and the fractional part:
[tex]\[ 3 \frac{1}{3} = 3 + \frac{1}{3} \][/tex]
To combine these, we can convert the integer to a fraction with the same denominator:
[tex]\[ 3 = \frac{3 \times 3}{3} = \frac{9}{3} \][/tex]
Now, add the fractional parts:
[tex]\[ \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \][/tex]
So, [tex]\( 3 \frac{1}{3} \)[/tex] as an improper fraction is [tex]\( \frac{10}{3} \)[/tex].
### Step 2: Convert the improper fraction to a decimal.
Next, convert [tex]\( \frac{10}{3} \)[/tex] to a decimal form for simplicity in multiplication:
[tex]\[ \frac{10}{3} \approx 3.3333333333333335 \][/tex]
### Step 3: Calculate the square root of 52.
Next, find the square root of 52:
[tex]\[ \sqrt{52} \approx 7.211102550927978 \][/tex]
### Step 4: Perform the multiplication.
Finally, multiply the results from step 2 and step 3 together:
[tex]\[ 3.3333333333333335 \times 7.211102550927978 \approx 24.03700850309326 \][/tex]
Thus, the result of the expression [tex]\( 3 \frac{1}{3} \times \sqrt{52} \)[/tex] is approximately [tex]\( 24.03700850309326 \)[/tex].
