Answer :
To solve the expression [tex]\(\sqrt[3]{0.027} + \sqrt[3]{125} + \sqrt[3]{0.729}\)[/tex], let's evaluate each cube root individually and then add the terms together.
1. Evaluate [tex]\(\sqrt[3]{0.027}\)[/tex]:
The cube root of [tex]\(0.027\)[/tex] is [tex]\(0.3\)[/tex]. This is because:
[tex]\[ 0.3 \times 0.3 \times 0.3 = 0.027 \][/tex]
2. Evaluate [tex]\(\sqrt[3]{125}\)[/tex]:
The cube root of [tex]\(125\)[/tex] is [tex]\(5.0\)[/tex]. This is because:
[tex]\[ 5 \times 5 \times 5 = 125 \][/tex]
3. Evaluate [tex]\(\sqrt[3]{0.729}\)[/tex]:
The cube root of [tex]\(0.729\)[/tex] is [tex]\(0.9\)[/tex]. This is because:
[tex]\[ 0.9 \times 0.9 \times 0.9 = 0.729 \][/tex]
Now, let's add these results together:
[tex]\[ 0.3 + 5.0 + 0.9 = 6.2 \][/tex]
So, the value of [tex]\(\sqrt[3]{0.027} + \sqrt[3]{125} + \sqrt[3]{0.729}\)[/tex] is [tex]\(6.2\)[/tex].
Thus, the correct answer is [tex]\( \boxed{6.2} \)[/tex].
1. Evaluate [tex]\(\sqrt[3]{0.027}\)[/tex]:
The cube root of [tex]\(0.027\)[/tex] is [tex]\(0.3\)[/tex]. This is because:
[tex]\[ 0.3 \times 0.3 \times 0.3 = 0.027 \][/tex]
2. Evaluate [tex]\(\sqrt[3]{125}\)[/tex]:
The cube root of [tex]\(125\)[/tex] is [tex]\(5.0\)[/tex]. This is because:
[tex]\[ 5 \times 5 \times 5 = 125 \][/tex]
3. Evaluate [tex]\(\sqrt[3]{0.729}\)[/tex]:
The cube root of [tex]\(0.729\)[/tex] is [tex]\(0.9\)[/tex]. This is because:
[tex]\[ 0.9 \times 0.9 \times 0.9 = 0.729 \][/tex]
Now, let's add these results together:
[tex]\[ 0.3 + 5.0 + 0.9 = 6.2 \][/tex]
So, the value of [tex]\(\sqrt[3]{0.027} + \sqrt[3]{125} + \sqrt[3]{0.729}\)[/tex] is [tex]\(6.2\)[/tex].
Thus, the correct answer is [tex]\( \boxed{6.2} \)[/tex].
