Square Root of 1444

In Mathematics, the square root of a number is a number, which when multiplied by itself results in the original number. Thus,the square root of 1444 is a number, which when multiplied by itself results in the original number 1444. The square root of 1444 is a rational number, as it can be expressed in the form of p/q. In this article, we are going to learn the square root of 1444 using two different methods such as the prime factorization method and the long division method in detail.

What is the Square Root of 1444?

If a number is multiplied by itself and gives the result as 1444, then the number is the square root 1444. The square root of 1444 is symbolically expressed as √1444.

Hence, √1444 = √(Number × Number)

Thus, if we multiply the number 38 two times, we get the original value 1444.

(i.e) √1444 = √(38× 38)

√1444 = √(38)²

Now, remove square and square root, we get

√1444 = ± 38

Square Root of 1444 in Radical Form

To express the square root of 1444 in the simplest radical form, write the prime factorization of 1444. The prime factorization of 1444 is 2×2×19×19. Thus, if we write the radical form (i.e) √(2×2×19×19), it should not be the simplest radical form. Therefore, the radical form of the square root of 1444 is √1444.

Square Root of 1444 by Prime Factorization Method

To find the square root of 1444 using the prime factorization method, we need to know the prime factorization of 1444. Thus, the prime factorization of 1444 is 2 × 2 × 19 × 19.

Thus, √1444 = √(2 × 2 × 19 × 19)

√1444 = (√2)².(√19)²

√1444 = 2×19

√1444 = 38

Hence, the square root of 1444 is equal to 38.

Square Root of 1444 by Long Division Method

The procedure to find the square root of 1444 using the long division method is given as follows:

Step 1: Write the number 1444 in decimal form. Now, pair the number 1444 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 14 by a number, such that the product of the same number should be less than or equal to 14. Thus, 3×3=9, which is less than 14. Thus, we obtained the quotient = 3 and remainder = 5.

Step 3: Double the quotient value, so we get 6 and assume that 60 is the new divisor. Now, bring down the value 44 for division operation. So, the new dividend obtained is 544. Now, find the number, such that (60 + new number) × new number should give the product value that should be less than or equal to 544. Hence, (60+8) × 8 = 544, which is equal to 544.

Step 4: Now subtract 544 from 544, and we get 00 as the new reminder, and 38 as a quotient.

Step 5: Thus, the value of the square root of 1444, √1444 is 38.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify √1444 + 40.

Solution:

Given: √1444 + 40

We know that the square root of 1444 is 38.

Now, substitute the value in the expression, we get:

√1444 + 40 = 38 + 40

√1444 + 40 = 78

Therefore, the simplified form of √1444 + 40 is 78.

Example 2:

Find the value of a, if a√1444 +25 = 170.

Solution:

Given: a√1444 +25 = 170.

We know that √1444 = 38

Now, substitute the value in the given equation, we get

a(38)+25 = 170

38a = 170-25

38a = 145

a = 145/38

a = 3.81578

a = 3.816 (Rounded to 3 decimal places).

Hence, the value of a is 3.816.

Example 3:

Simplify the expression: 2√1444+10.

Solution:

Given expression: 2√1444 + 10

We know that √1444 = 38.

Now, substitute the value in the given expression, we get

2√1444 +10 = 2(38) + 10

2√1444 +10 = 76+10

2√1444 + 10 = 86.

Hence, the simplified form of 2√1444+10 is 86.