Question

How do you solve $5\sqrt{x+1}=21$?

Answer 1

Hint: Now to solve the given equation we will first separate the constant terms and the square root terms in the equation by dividing the equation by 5. Then we will square the equation and simplify. Now we will again separate the variables and constants and simplify the equation till we get the value of x.

Complete step by step answer:
Now first consider the given equation $5\sqrt{x+1}=21$
This is an equation in one variable. To solve the equation we will have to separate the constant and root terms and then square the equation on both sides.
First we will try to separate the root and the integer terms. To do so we will divide the whole equation by 5. Hence we get,
$\Rightarrow \sqrt{x+1}=\dfrac{21}{5}$
Now squaring the whole equation we get, $x+1=\dfrac{{{21}^{2}}}{{{5}^{2}}}$
Hence we get the equation as, $x+1=\dfrac{441}{25}$
Now we will subtract 1 on both sides of the equation. Hence we get,
$\Rightarrow x=\dfrac{441}{25}-1$
Now to simplify the equation we will take LCM in the above equation. Hence we get,
$\begin{align}
  & \Rightarrow x=\dfrac{441-25}{25} \\
 & \Rightarrow x=\dfrac{416}{25} \\
\end{align}$
Hence we have the value of x.

Note:
Note that we can also directly square the equation on both sides first. This will give us the equation. $25\left( x+1 \right)=441$ . Now we will solve this equation by trying to separate the variable from all other constants. To do so we will first divide the whole equation by 25 and then we will subtract 1 on both sides of the equation.