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The square root of which of the following is a rational number? (SSC Sub. Ins. 2018)
- a)5823.82
- b)1489.96
- c)22504.9
- d)2460.14
Correct answer is option 'B'. Can you explain this answer?
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The square root of which of the following is a rational number? (SSC...
Finding Rational Numbers in Square Root
Explanation:
To find out which of the given options has a rational square root, we need to follow the steps given below:
Step 1: Prime Factorization
We need to find the prime factorization of the given options. The prime factorization of each option is given below:
a) 5823.82 = 2 × 3 × 971.303
b) 1489.96 = 2 × 2 × 2 × 7 × 53.21
c) 22504.9 = 2 × 2 × 2 × 11 × 509.29
d) 2460.14 = 2 × 2 × 5 × 123.007
Step 2: Pairing of Prime Factors
Next, we need to pair the prime factors in groups of two. If there is any prime factor left unpaired, it means that the number has an irrational square root. The pairing of prime factors for each option is given below:
a) 2 × 3, 971.303 (irrational)
b) 2 × 2, 7 × 53.21 (rational)
c) 2 × 2, 11 × 509.29 (irrational)
d) 2 × 2, 5 × 123.007 (irrational)
Step 3: Simplification of Rational Square Root
We can simplify the rational square root by taking out the pair of prime factors outside the square root sign. For example, the square root of 2 × 2 × 7 × 53.21 can be simplified as 2 × 53.21 = 106.42. Therefore, the only option which has a rational square root is option B, which is 1489.96.
Therefore, the correct answer is option B, which is 1489.96.
Explanation:
To find out which of the given options has a rational square root, we need to follow the steps given below:
Step 1: Prime Factorization
We need to find the prime factorization of the given options. The prime factorization of each option is given below:
a) 5823.82 = 2 × 3 × 971.303
b) 1489.96 = 2 × 2 × 2 × 7 × 53.21
c) 22504.9 = 2 × 2 × 2 × 11 × 509.29
d) 2460.14 = 2 × 2 × 5 × 123.007
Step 2: Pairing of Prime Factors
Next, we need to pair the prime factors in groups of two. If there is any prime factor left unpaired, it means that the number has an irrational square root. The pairing of prime factors for each option is given below:
a) 2 × 3, 971.303 (irrational)
b) 2 × 2, 7 × 53.21 (rational)
c) 2 × 2, 11 × 509.29 (irrational)
d) 2 × 2, 5 × 123.007 (irrational)
Step 3: Simplification of Rational Square Root
We can simplify the rational square root by taking out the pair of prime factors outside the square root sign. For example, the square root of 2 × 2 × 7 × 53.21 can be simplified as 2 × 53.21 = 106.42. Therefore, the only option which has a rational square root is option B, which is 1489.96.
Therefore, the correct answer is option B, which is 1489.96.
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