Question

find the square root of 441 using prime factorisation and long division method​

Answer 1

Answer:

The square root of 441 is 21

Step-by-step explanation:

Given: Number 441

Find: Square root of 441 by prime factorization method

Solution:

First we factor 441

441= 3x3x7x7

441= 3^2 x 7^2

Taking root both side

√441= √3^2x7^2

√441= 3x7

√441= 21

Answer 2

Answer:

Square Root of 441 by Prime Factorization Method

The following steps can be followed to find the square root of 441 using prime factorization:

Step 1. Determine the prime factorization of 441.

441 = 3 × 3 × 7 × 7

441 = 32 × 72

Step 2. Group the prime factors of 441 in pairs.

441 = 32 × 72

Step 3. Pick one factor from each pair and the square root of 441 can be written as:

√441 = √(32 × 72)

√441 = √(3 × 7)2

√441 = ((3 × 7)2)1/2 = ±(3 × 7)

√441 = ±21

Square Root of 441 by Long Division

Follow the steps shown below to find the square root of 441 by long division.

Step 1. Write 441 as shown in the figure. Pair the number from the right end (1) by putting a bar on top of them. In the case of 441, 41 will be paired under one bar and 4 under the second bar.

Step 2. Find a number that when multiplied by itself results in a number equal to or less than 4.

Step 3. Drag the next pair of numbers. Here it is 41.

Multiply the quotient 2 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 in such a way that when it is multiplied with the new divisor, it results in 41 or a smaller number closest to 41.

Here the number is 1 as 41 × 1 = 41.

So, we get the value of the square root of √441 = 21 by the long division method.

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