Answer :
Sure! Let's solve the equation step by step:
The given equation is:
[tex]\[ 2 \sqrt[5]{x} + 7 = 15 \][/tex]
Step 1: Isolate the radical term.
Subtract 7 from both sides of the equation:
[tex]\[ 2 \sqrt[5]{x} = 15 - 7 \][/tex]
[tex]\[ 2 \sqrt[5]{x} = 8 \][/tex]
Step 2: Remove the coefficient of the radical term.
Divide both sides by 2:
[tex]\[ \sqrt[5]{x} = \frac{8}{2} \][/tex]
[tex]\[ \sqrt[5]{x} = 4 \][/tex]
Step 3: Eliminate the fifth root by raising both sides of the equation to the power of 5:
[tex]\[ x = 4^5 \][/tex]
Step 4: Calculate [tex]\(4^5\)[/tex]:
[tex]\[ 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 \][/tex]
Therefore, the solution to the equation [tex]\(2 \sqrt[5]{x} + 7 = 15\)[/tex] is [tex]\(x = 1024\)[/tex].
The given equation is:
[tex]\[ 2 \sqrt[5]{x} + 7 = 15 \][/tex]
Step 1: Isolate the radical term.
Subtract 7 from both sides of the equation:
[tex]\[ 2 \sqrt[5]{x} = 15 - 7 \][/tex]
[tex]\[ 2 \sqrt[5]{x} = 8 \][/tex]
Step 2: Remove the coefficient of the radical term.
Divide both sides by 2:
[tex]\[ \sqrt[5]{x} = \frac{8}{2} \][/tex]
[tex]\[ \sqrt[5]{x} = 4 \][/tex]
Step 3: Eliminate the fifth root by raising both sides of the equation to the power of 5:
[tex]\[ x = 4^5 \][/tex]
Step 4: Calculate [tex]\(4^5\)[/tex]:
[tex]\[ 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 \][/tex]
Therefore, the solution to the equation [tex]\(2 \sqrt[5]{x} + 7 = 15\)[/tex] is [tex]\(x = 1024\)[/tex].
