Question

How do you evaluate $ - {7^2}$

Answer 1

Hint: This is a basic numerical in which the only catch point is the negative sign. The sign is given to confuse the students. It is beneficial for the student to consider this as ${( - 7)^2}$. The student should be quick enough to understand this step and then proceed with the normal calculation. Though this is a basic numerical, problems would be asked where the numbers would be larger and involve more number of operations.

Complete step-by-step answer:
In order to solve such a type of sum, the first step would be to bring it in the form which is understandable.
The first step would be to take the negative sign inside the bracket .
$ - {7^2} = {( - 7)^2}$
Above step can also be written as ${( - 7)^2} = {( - 1)^2} \times {( - 7)^2}$
As we know that the square of a negative number is positive, we can say that ${( - 1)^2}$is $1$.
Thus the value of $ - {7^2}$ is the same as ${7^2}$ and its value is $49$.
Thus the answer to this question is $49$

Note: This is just the basic sum to understand how the negative sign works. Actual sum for which the student should prepare would be of the type $ - {3^2} \times {2^{ - 2}} - {( - 2)^3}$. These types of sums would also involve application of BODMAS rule. A thorough understanding of this rule would help the student to evaluate the sums involving negative signs correctly. Also students should keep in mind that the square of a negative number is always a positive number, whereas the cube of a negative number is always a negative number.