Step-by-step explanation:

How to Find the Square Root of 144?

The square of 144 can be calculated using the prime factorization method, long division method, or repeated subtraction method.

Square Root of 144 by Prime Factorization Method

The following steps can be followed to find the square root of 144 using prime factorization:

Step 1. Determine the prime factors of 144.

144 = 2 × 2 × 2 × 2 × 3 × 3

144 = 24 × 32

Step 2. Group the prime factors of 144 in pairs.

144 = 22 × 22 × 32

Step 3. Pick one factor from each pair and the square root of 144 can be written as:

√144 = √(22 × 22 × 32)

√144 = √(2 × 2 × 3)2

√144 = ((2 × 2 × 3)2)1/2 = ±(2 × 2 × 3)

√144 = ±12

Square Root of 144 by Long Division

Follow the steps shown below to find the square root of 144 by long division.

Step 1. Write 144 as shown in the figure. Start pairing the number in pairs of two digits from the right end by putting a bar on top of them. The unpaired number left in the left can be treated as a single entity as shown below. In the case of 144, 44 will be grouped under one bar and 1 under the second bar.

Step 2. Find a number which when multiplied by itself results in a number equal to or less than 1.

Step 3. Bring down the next pair of numbers. Here it is 44.

Multiply the quotient 1 by 2 (or add with itself) and write it as the new divisor’s ten’s place digit.

Step 4. Choose a number for the unit’s place of the divisor such that when it is multiplied with the new divisor, it will give 44 or a smaller number closest to 44.

Here the number is 22 as 22 × 2 = 44.

Explore square roots using illustrations and interactive examples.

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Important Notes:

The square root of 144 is represented as √144 in radical form and as (144)1/2 in exponential form.

The square root of any number is both negative and positive for the same numerical value. The square root of 144 is +12 and -12.

There will be n/2 digits in the square root of an even number with n digits.

There will be (n+2)/2 digits in the square root of an odd number with n digits

Challenging Questions:

Jason is running on a square ground with an area of 144 square feet. How much more he would have to run if later he wants to run on a square ground of area 441 square feet?