Question
Solve the equations
^5 square root of X+3=17
^5 square root of X+3=17
Answers
GPT-4o mini
To solve the equation \( \sqrt[5]{x} + 3 = 17 \), we first isolate the fifth root term. Here's how we do it step-by-step:
1. Subtract 3 from both sides of the equation:
\[
\sqrt[5]{x} = 17 - 3
\]
\[
\sqrt[5]{x} = 14
\]
2. Now, to eliminate the fifth root, raise both sides to the power of 5:
\[
x = 14^5
\]
3. Calculate \( 14^5 \):
\[
14^5 = 537824
\]
So, the solution to the equation \( \sqrt[5]{x} + 3 = 17 \) is
\[
\boxed{537824}
\]
1. Subtract 3 from both sides of the equation:
\[
\sqrt[5]{x} = 17 - 3
\]
\[
\sqrt[5]{x} = 14
\]
2. Now, to eliminate the fifth root, raise both sides to the power of 5:
\[
x = 14^5
\]
3. Calculate \( 14^5 \):
\[
14^5 = 537824
\]
So, the solution to the equation \( \sqrt[5]{x} + 3 = 17 \) is
\[
\boxed{537824}
\]