Compare Your Answers

\(\begin{align}
 y - 1 &\ge 0 \\
 y &\ge 1, y \in \rm R \\
 \end{align}\)

\(\begin{align}
 \sqrt {y - 1} &= 7 \\
 \left( {\sqrt {y - 1} } \right)^2 &= 7^2  \\
 y - 1 &= 49 \\
 y &= 50 \\
 \end{align}\)

Verify:

Left Side	Right Side
\(\begin{array}{r}  \sqrt {y - 1}  \\  \sqrt {50 - 1}  \\  \sqrt {49}  \\  7 \\  \end{array}\)	\(7\)
LS = RS

Because the index is \(5\) (odd), there are no restrictions on the variable, \(x \in \rm R\).

\(\begin{align}
 \sqrt[5]{{4x}} &= 2 \\
 \left( {\sqrt[5]{{4x}}} \right)^5 &= 2^5  \\
 4x &= 32 \\
 x &= 8 \\
 \end{align}\)

Verify:

Left Side	Right Side
\(\begin{array}{r}  \sqrt[5]{{4x}} \\  \sqrt[5]{{4\left( 8 \right)}} \\  \sqrt[5]{{32}} \\  2 \\  \end{array}\)	\(2\)
LS = RS\(\hspace{30pt}\)