Question

How do you Simplify \[\sqrt{\dfrac{49}{121}}\]?

Answer 1

Hint: Factorise both numerator and denominator and then by pairing the numbers determine the value of square root of numerator and denominator.
Like, \[\sqrt{\dfrac{4}{9}}\] if we have to determine the value of the expression,
Then prime factoring the numerator and denominator we will get,
\[\sqrt{\dfrac{4}{9}}=\sqrt{\dfrac{2\times 2}{3\times 3}}=\dfrac{2}{3}\]
Apply this to determine the value of a given expression.

Complete step by step solution:
As per data given in the question,
We have to determine the value of \[\sqrt{\dfrac{49}{121}}\]
As we know that,
Prime factorisation of \[49\] is \[7\times 7\].
The factorisation of \[121\] is \[11\times 11\].
So, we will put this value in the expression instead of \[49\] and \[121\].
We will get,
\[\sqrt{\dfrac{7\times 7}{11\times 11}}\]
As we know that,
If two similar terms are multiplied under square root then when we solve the square root only one number between two similar terms comes out.
Like, if \[\sqrt{4}=\sqrt{2\times 2}=2\]
Like here two \[2\] are under square root so when we solve the square root only one \[2\] comes out.
So, applying this concept in the expression given in the question,
We will get,
\[\Rightarrow \sqrt{\dfrac{7\times 7}{11\times 11}}\]
\[\Rightarrow \]\[\dfrac{7}{11}\]

Hence, we can say that value of \[\sqrt{\dfrac{49}{121}}\] will be \[\dfrac{7}{11}\].

Note: While converting the number into form of factors make sure you are taking multiplication of similar number,
Like if we have to find the square root of \[\sqrt{16}=2\times 8\] so such conversion of \[16\] must be avoided.
As we have to take similar numbers as much possible, so that square root can be easily determined.
So, the factorisation of \[\sqrt{16}\] will be \[\sqrt{2\times 2\times 2\times 2}=2\times 2=4\].