Question

How do you simplify $\sqrt{x+1}=5$?

Answer 1

Hint: To solve the above question we will use the concept of algebra. Since, we have to find the value of x and we have a square root of (x + 1). We will first square both sides of the given equation and then we will take 1 from the LHS to the RHS and then we get the value of x.

Complete step-by-step solution:
We will use the concept of algebraic equations to solve the above question. Since, we have to find the value of x by simplifying the above equation $\sqrt{x+1}=5$.
At first, we will square the equation given in the question both side because without removing square root we cannot simplify the given equation
So, after squaring both sides the given equation we will get:
$\Rightarrow {{\left( \sqrt{x+1} \right)}^{2}}={{\left( 5 \right)}^{2}}$
Now, we know that $\sqrt{a}={{\left( a \right)}^{\dfrac{1}{2}}}$ so we will write $\sqrt{x+1}={{\left( x+1 \right)}^{\dfrac{1}{2}}}$
$\Rightarrow {{\left( x+1 \right)}^{\dfrac{1}{2}\times 2}}={{\left( 5 \right)}^{2}}$
Now, after simplifying we will get:
$\Rightarrow \left( x+1 \right)=25$
Now, we will subtract 1 from the both sides of the equation to eliminate 1 from the Left-Hand Side of the given equation.
$\Rightarrow x+1-1=25-1$
So, $x = 25 – 1 = 24$.
Hence, x = 24 is the solution of the equation given.
This is our required solution.

Note: Students are required to note that when we have radicals in the algebraic equation then we always first try to eliminate that square root or radical by squaring the equation after arranging some terms so that we get the simplified equation which is easily solvable.