Question

How do you solve \[{{\left( x+4 \right)}^{2}}=81\] using the square root property?

Answer 1

Hint:In this problem, we have to solve and find the value of x by using the square root property. We can first take the square root on both the left-hand side and the right-hand side of the equation. We can then cancel the square root on the left-hand side and write the number which is square of 81 on the right-hand side. We can then subtract 4 on both sides to get the value of x.

Complete step by step solution:
We know that the given equation to be solved is
\[{{\left( x+4 \right)}^{2}}=81\]
We can now take square root on both the left-hand side and the right-hand side of the equation, we get
\[\Rightarrow \sqrt{{{\left( x+4 \right)}^{2}}}=\sqrt{81}\]
We can now cancel the square root and the square on the left-hand side and write the number which is square of 81 in the right-hand side, we get
\[\Rightarrow x+4=\sqrt{{{9}^{2}}}\text{ }\because {{\text{9}}^{2}}=81\]
We can now cancel the square and the square root on the right-hand side, we get
\[\Rightarrow x+4=9\]
We can now subtract 4 on both sides, we get
\[\Rightarrow x=9-4=5\]
Therefore, the value of x = 5.

Note: We should know that we can cancel the square and the square root as the square root is nothing but the half to the power. We can now check whether the result is correct by substituting it in the given equation.
We can now substitute x = 5 in the given equation, we get
\[\begin{align}
  & \Rightarrow {{\left( 5+4 \right)}^{2}}=81 \\
 & \Rightarrow {{9}^{2}}=81 \\
 & \Rightarrow 81=81 \\
\end{align}\]
Therefore, the value of x is correct.