Question

How do you solve this equation using the square root property \[{{\left( x+5 \right)}^{2}}=36\]?

Answer 1

Hint: From the question given, we have been asked to solve the given equation \[{{\left( x+5 \right)}^{2}}=36\] using the square root property. First of all, to solve the above given question, we have to know about the square root property. Then after applying the square root property to the given equation, we have to simplify further and solve to get the solution for the given equation.
Square root property: The square root property involves taking the square root of both the terms on either side of the equation.

Complete step-by-step answer:
From the question, we have been given that \[{{\left( x+5 \right)}^{2}}=36\]
Now, apply the square root property to the above given equation.
Square root property: The square root property involves taking the square root of both the terms on either side of the equation.
After applying the square root property to the given equation, we get \[\Rightarrow \sqrt{{{\left( x+5 \right)}^{2}}}=\sqrt{36}\]
Now, simplify further to get the exact and accurate solution for the given equation.
By simplifying further, we get \[\Rightarrow x+5=\pm 6\]
Now, shift \[5\] from the left hand side of the equation to the right hand side of the equation. By shifting \[5\] from left hand side of the equation to the right hand side of the equation, we get
\[\Rightarrow x=\pm 6-5\]
Therefore, \[x=1\text{ or x=-11}\]
Hence, we got the solutions for the given equation by using the square root property.

Note: We should be well known about the square root property. Also, we should be well aware of the usage of the square root property. Also, we should be very careful while doing the calculation part. Also, we should be very careful while simplifying the equation, after applying the square root property. After solving by verifying it we can be sure with our answer. For this question we have the equation \[{{\left( x+5 \right)}^{2}}=36\] and the values of $x=1$ and $x=-11$ . By substituting $x=1$ in the equation we will have $\Rightarrow {{\left( 1+5 \right)}^{2}}={{6}^{2}}\Rightarrow 36$ and by substituting $x=-11$ we will have $\Rightarrow {{\left( -11+5 \right)}^{2}}={{\left( -6 \right)}^{2}}\Rightarrow 36$ . Hence the solution is verified.