Question

To eliminate the square root in the equation $2x+1=\sqrt{x+1}$, we ___ each side to get the equation ___

Short answer

To eliminate the square root in the equation $2x+1=\sqrt{x+1}$, we square each side to get the equation${\left(2x+1\right)}^2=x+1$

Step-by-step solution

Step 1. Apply the concept of radicals.

A radical equation is an equation in which a variable is under a radical. To solve a radical equation, isolate the radical expression involving the variable.

Step 2. Analyze the given expression.

Given

$2x+1=\sqrt{x+1}$

The radical is isolated.

Step 3. Solve.

To eliminate the square root, we first square each side of the equation:

$\begin{array}{l}2x+1=\sqrt{x+1}\\ \Rightarrow {\left(2x+1\right)}^2={\left(\sqrt{x+1}\right)}^2\\ \Rightarrow {\left(2x+1\right)}^2=x+1\end{array}$