Question

The square root of 144 is
(a) 114
(b) 442
(c) 12
(d) 24

Answer 1

Hint: Write prime factorization of the number 144 and take out one term from each of the terms that occur in pairs. Multiply all the chosen terms to get the square root of 144.

Complete step-by-step solution -
We have to calculate the square root of 144.
We will firstly write the prime factorization of 144.
To write the prime factorization of any number, start by dividing the number by the first prime number, which is 2 and then continue to divide by 2 until you get a number which is not divisible by 2 (which means that you get a decimal or remainder on dividing the number by 2). Then start dividing the number by the next prime number which is 3. Continue dividing the number by 3 until you get a number which is not divisible by 3. Thus, continuing the process, keep dividing the numbers by series of prime numbers until the only numbers left are prime numbers. Write the given number as a product of all the prime numbers (considering the fact to count each prime number as many times as it divides the given number) to get the prime factorization of the given number.
Thus, the prime factorization of 144 is . We will now take out one term from each of the terms that occur in pairs.
By taking out one term from each of the terms that occur in pairs, we have .
Thus, the square roots of 144 is .
Hence, the square root of 144 is 12, which is option (c).

Note: We can also calculate the square root of 144 by a long division method in which each term is paired before finding out the square root and then we find the appropriate number which divides the paired number.