Question

How do you simplify \[\sqrt {75} \] ?

Answer 1

Hint: The square and square root are inverse to each other. Here in this we have a symbol \[\sqrt {} \] , this symbol represents the square root. Here we have to find the square root of 75. So first we simplify the number 75 by using the factorisation and then we simplify the number \[\sqrt {75} \] .

Complete step-by-step answer:
In the question we can see the \[\sqrt {} \] symbol. This symbol represents the square root. A square root is defined as a number which produces a specified quantity when multiplied by itself. The number which is in the square root is 75. The number 75 is not a perfect square. The perfect square is defined as the number expressed as the square of a number. Since the number 75 is not a perfect square we factorise the number 75.

5	75
5	15
3	3
	1

Therefore, the number can be written as \[75 = 5 \times 5 \times 3\] . Here 5 is multiplied twice so we can write in the exponential form.
So, we have \[75 = {5^2} \times 3\]
Therefore \[\sqrt {75} = \sqrt {{5^2} \times 3} \] ---- (1)
Here we apply the property of square root that is \[\sqrt {a \times b} = \sqrt a \times \sqrt b \] , on applying this property the equation (1) is written as \[\sqrt {75} = \sqrt {{5^2}} \times \sqrt 3 \] ----- (2)
As we know that the square and square root are inverse to each other. The square root will cancel in the equation (2)
So, we have \[\sqrt {75} = 5\sqrt 3 \]
Hence, we have obtained the simplified form. Therefore the \[\sqrt {75} = 5\sqrt 3 \] .
So, the correct answer is “$5\sqrt 3$”.

Note: When we want to find the square root of some number, let it be x. If x is a perfect square then we can obtain the result directly. Otherwise if x is not a perfect square let we factorise the x and if it possible we write the number in the form of exponential and then we simplify the number