Correct Answer - Option 4 :
\(\frac{34}{11}\)
Given:
Our given expression is \(9 \frac{67}{121}\)
Calculation:
Converting mixed fraction to the fraction,
Our given expression is \(9 \frac{67}{121}\)
⇒ (9 × 121 + 67)/121
⇒ 1156/121
Using prime factorization in numerator and denominator,
1156 = 2 × 2 × 17 × 17
And, 121 = 11 × 11
The square root of the given number = (1156/121)1/2
⇒ {(2 × 2 × 17 × 17)/(11 × 11)}1/2
⇒ 34/11
∴ The square root of the given expression is 34/11
