Square Root of 1089

The square root of 1089 is a number, which when multiplied by itself results in the original number 1089. The square root of 1089 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 1089 using two different methods such as the prime factorization method and the long division method with complete explanation.

What is the Value of Square Root of 1089?

If a number is multiplied by itself and gives the result as 1089, then the number is the square root 1089. The square root of 1089 is symbolically expressed as √1089.

Hence, √1089 = √(Number × Number)

Thus, if we multiply the number 33 two times, we get the original value 1089.

(i.e) √1089 = √(33× 33)

√1089 = √(33)²

Now, remove square and square root, we get

√1089 = ± 33

Square Root of 1089 in Radical Form

To express the square root of 1089 in the simplest radical form, write the prime factorization of 1089. The prime factorization of 1089 is 3×3×11×11. Thus, if we write the radical form (i.e) √(3×3×11×11), it should not be the simplest radical form. Therefore, the radical form of the square root of 1089 is √1089.

Square Root of 1089 by Prime Factorization Method

To find the square root of 1089 using the prime factorization method, we need to know the prime factorization of 1089. Thus, the prime factorization of 1089 is 3 × 3 × 11 × 11.

Thus, √1089 = √(3 × 3 × 11 × 11)

√1089 = (√3)².(√11)²

√1089 = 3×11

√1089 = 33

Hence, the square root of 1089 is equal to 33.

Square Root of 1089 by Long Division Method

The procedure to find the square root of 1089 using the long division method is given as follows:

Step 1: Write the number 1089 in decimal form. Now, pair the number 1089 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 10 by a number, such that the product of the same number should be less than or equal to 10. Thus, 3×3=9, which is less than 10. Thus, we obtained the quotient = 3 and remainder = 1.

Step 3: Double the quotient value, so we get 6 and assume that 60 is the new divisor. Now, bring down the value 89 for division operation. So, the new dividend obtained is 189. Now, find the number, such that (60 + new number) × new number should give the product value that should be less than or equal to 189. Hence, (60+3) × 3 = 189, which is equal to 189.

Step 4: Now subtract 189 from 189, and we get 00 as the new reminder, and 33 as a quotient.

Step 5: Thus, the value of the square root of 1089, √1089 is 33.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify 5√1089 + 10.

Solution:

Given: 5√1089 + 10

We know that the square root of 1089 is 33.

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

5√1089 + 10 = 5(33) + 10

5√1089 + 10 = 165 + 10 = 175

Therefore, the simplified form of 5√1089 + 10 is 175.

Example 2:

Find the value of k, if k√1089 = 99.

Solution:

Given: k√1089 = 99.

We know that √1089 = 33

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

k(33) = 99

k = 99/33

k = 3.

Hence, the value of k is 3.

Example 3:

Simplify the expression: (3√1089 × 2√1089)

Solution:

Given expression: (3√1089 × 2√1089)

(3√1089 × 2√1089) = 6(√1089)²

On removing square and square root, we get

(3√1089 × 2√1089) = 6(1089) = 6534

Hence, the simplified form of (3√1089 × 2√1089) is 6534.