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Sagot :
Sure! Let's break down the expression step-by-step to find the value of [tex]\( 2^2 + \sqrt{\frac{16}{9}} - \frac{1}{3} \)[/tex].
### Step 1: Calculating [tex]\( 2^2 \)[/tex]
First, we calculate [tex]\( 2^2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
### Step 2: Calculating [tex]\( \sqrt{\frac{16}{9}} \)[/tex]
Next, we find the square root of [tex]\( \frac{16}{9} \)[/tex].
First, we simplify [tex]\( \frac{16}{9} \)[/tex]:
[tex]\[ \frac{16}{9} = \frac{4^2}{3^2} \][/tex]
Then, we take the square root:
[tex]\[ \sqrt{\frac{16}{9}} = \sqrt{\frac{4^2}{3^2}} = \frac{4}{3} = 1.3333333333333333 \][/tex]
### Step 3: Calculating [tex]\( \frac{1}{3} \)[/tex]
Next, we calculate [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ \frac{1}{3} = 0.3333333333333333 \][/tex]
### Step 4: Combining All Terms
Now, we combine all the terms in the expression:
[tex]\[ 4 + \sqrt{\frac{16}{9}} - \frac{1}{3} \][/tex]
Substituting the values we calculated:
[tex]\[ 4 + 1.3333333333333333 - 0.3333333333333333 \][/tex]
Performing the addition and subtraction:
[tex]\[ 4 + 1.3333333333333333 = 5.333333333333333 \][/tex]
[tex]\[ 5.333333333333333 - 0.3333333333333333 = 5 \][/tex]
### Final Answer
So, the value of the expression [tex]\( 2^2 + \sqrt{\frac{16}{9}} - \frac{1}{3} \)[/tex] is:
[tex]\[ 5 \][/tex]
### Step 1: Calculating [tex]\( 2^2 \)[/tex]
First, we calculate [tex]\( 2^2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
### Step 2: Calculating [tex]\( \sqrt{\frac{16}{9}} \)[/tex]
Next, we find the square root of [tex]\( \frac{16}{9} \)[/tex].
First, we simplify [tex]\( \frac{16}{9} \)[/tex]:
[tex]\[ \frac{16}{9} = \frac{4^2}{3^2} \][/tex]
Then, we take the square root:
[tex]\[ \sqrt{\frac{16}{9}} = \sqrt{\frac{4^2}{3^2}} = \frac{4}{3} = 1.3333333333333333 \][/tex]
### Step 3: Calculating [tex]\( \frac{1}{3} \)[/tex]
Next, we calculate [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ \frac{1}{3} = 0.3333333333333333 \][/tex]
### Step 4: Combining All Terms
Now, we combine all the terms in the expression:
[tex]\[ 4 + \sqrt{\frac{16}{9}} - \frac{1}{3} \][/tex]
Substituting the values we calculated:
[tex]\[ 4 + 1.3333333333333333 - 0.3333333333333333 \][/tex]
Performing the addition and subtraction:
[tex]\[ 4 + 1.3333333333333333 = 5.333333333333333 \][/tex]
[tex]\[ 5.333333333333333 - 0.3333333333333333 = 5 \][/tex]
### Final Answer
So, the value of the expression [tex]\( 2^2 + \sqrt{\frac{16}{9}} - \frac{1}{3} \)[/tex] is:
[tex]\[ 5 \][/tex]
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