Question

How do you solve \[{x^2} = 90\] ?

Answer 1

Hint: The given question is to solve by using the factorization method, once we factorize the number given then after making the square then solve the given equation by putting the root over the number and then we can get the solution for the given expression.

Complete step by step solution:
The given question is \[{x^2} = 90\]
Here we need to solve the question by factoring the given number and then pair the numbers and then solve the given expression, on factoring we get:
 \[ \Rightarrow 90 = 2 \times 3 \times 3 \times 5\]
Here we can see that the given number three is in pair and rest multiple two and five are in single form, and not in the pair, hence only three can be come out from the root and rest two and five multiple will be inside bracket, on solving this into mathematical expression we get:
 \[
   \Rightarrow {x^2} = 90 \\
   \Rightarrow x = \sqrt {90} = \sqrt {2 \times 3 \times 3 \times 5} = 3\sqrt {10} \;
 \]
Here we get the value for the given expression, and we get the root value for the given number.
So, the correct answer is “$3\sqrt {10}$”.

Note: The given question can also be simplified by the divisible method rule, in which we need to get the result for the root value of a number by using a divisible method.
The given expression needs to be solved by using the factorization method, here we can also get the solution for this expression directly if the given number can be converted into square form then we can directly write the solution for the root solution for the given number.