Question

Find the value of$\sqrt {49} - \sqrt {25} $.
$
  {\text{A}}{\text{. }}\sqrt 3 \\
  {\text{B}}{\text{. }} - \sqrt 3 \\
  {\text{C}}{\text{. }}2 \\
  {\text{D}}{\text{. None of these}} \\
 $

Answer 1

Hint: Here we go through by finding the square root of the number that is given in under the root. We can find its root by factoring the number. And we know that a square root of a number is a value that can be multiplied by itself to give the original number.

Complete Step-by-Step solution:
Now in the question we have to find $\sqrt {49} - \sqrt {25} $,
We can write $\sqrt {49} $ as $\sqrt {7 \times 7} $ by factoring the 49 it can be written as $7 \times 7$.
Now we can write $\sqrt {25} $ as $\sqrt {5 \times 5} $ by factoring the 25 it can be written as $5 \times 5$.
As we know that a square root of a number is a value that can be multiplied by itself to give the original number.
So we can say $\sqrt {49} = \sqrt {7 \times 7} = 7$
And $\sqrt {25} = \sqrt {5 \times 5} = 5$
Put these values in the question,
$
  \sqrt {49} - \sqrt {25} \\
   = \sqrt {7 \times 7} - \sqrt {5 \times 5} \\
   = 7 - 5 \\
   = 2 \\
 $
Hence option C is the correct answer.

Note: Whenever we face such a type of question the key concept for solving the question is to find out the square roots that are given in the roots and then put these values in the question to get the answer. And always keep in mind the properties of squares that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since ${( - 3)^2} = {( + 3)^2} = 9$. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root and is written $r = {(x)^{\dfrac{1}{2}}}$ or $r = \sqrt x $. "The'' square root is generally taken to mean the principal square root.