Square Root of 1764

The square root of 1764 is a number, which when multiplied by itself results in the original number 1764. The square root of 1764 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 1764 using two different methods such as the prime factorization method and the long division method with complete explanation.

Table of Contents:

• What is the Square Root of 1764?
• Square Root of 1764 in Radical Form
• Square Root of 1764 by Prime Factorization Method
• Square Root of 1764 by Long Division Method
• Examples
• FAQs

What is the Square Root of 1764?

If a number is multiplied by itself and gives the result as 1764, then the number is the square root 1764. The square root of 1764 is symbolically expressed as √1764.

Hence, √1764 = √(Number × Number)

Thus, if we multiply the number 42 two times, we get the original value 1764.

(i.e) √1764 = √(42× 42)

√1764 = √(42)²

Now, remove square and square root, we get

√1764 = ± 42

Square Root of 1764 in Radical Form

To express the square root of 1764 in the simplest radical form, write the prime factorization of 1764. The prime factorization of 1764 is 2×2×3×3×7×7. Thus, if we write the radical form (i.e) √(2×2×3×3×7×7), it should not be the simplest radical form. Therefore, the radical form of the square root of 1764 is √1764.

Square Root of 1764 by Prime Factorization Method

To find the square root of 1764 using the prime factorization method, we need to know the prime factorization of 1764. Thus, the prime factorization of 1764 is 2×2×3×3×7×7.

Thus, √1764 = √( 2×2×3×3×7×7)

√1764 = (√2)².(√3)².(√7)²

√1764 = 2×3×7

√1764 = 42

Hence, the square root of 1764 is equal to 42.

Square Root of 1764 by Long Division Method

The procedure to find the square root of 1764 using the long division method is given as follows:

Step 1: Write the number 1764 in decimal form. Now, pair the number 1764 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 17. Thus, 4×4=16, which is less than 17. Thus, we obtained the quotient = 4 and remainder = 1.

Step 3: Double the quotient value, so we get 8 and assume that 80 is the new divisor. Now, bring down the value 64 for division operation. So, the new dividend obtained is 164. Now, find the number, such that (80 + new number) × new number should give the product value that should be less than or equal to 164. Hence, (80+2) × 2 = 164, which is equal to 164.

Step 4: Now subtract 164 from 164, and we get 00 as the new reminder, and 42 as a quotient.

Step 5: Thus, the value of the square root of 1764, √1764 is 42.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify 10√1764 – 5.

Solution:

Given: 10√1764 – 5

We know that the square root of 1764 is 42.

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

10√1764 – 5 = 10(42) – 5

10√1764 – 5 = 420-5 = 415

Therefore, the simplified form of 10√1764 – 5 is 415.

Example 2:

Find the value of a, if a√1764 = 84.

Solution:

Given: a√1764 = 84.

We know that √1764 = 42

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

a(42) = 84

a = 84/42

a = 2.

Hence, the value of a is 2.

Example 3:

Simplify the expression: (2√1764 × 2√1764)

Solution:

Given expression: (2√1764 × 2√1764)

(2√1764 × 2√1764) = 4(√1764)²

On removing square and square root, we get

(2√1764 × 2√1764) = 4(1764) = 7056

Hence, the simplified form of (2√1764 × 2√1764) is 7056.