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Square Root of 1764

The square root of 1764 is expressed as √1764 in the radical form and as (1764)^½ or (1764)^0.5 in the exponent form. The square root of 1764 is 42. It is the positive solution of the equation x² = 1764. The number 1764 is a perfect square.

Square Root of 1764: 42
Square Root of 1764 in exponential form: (1764)^½ or (1764)^0.5
Square Root of 1764 in radical form: √1764

Square Root of 1764

1.	What is the Square Root of 1764?
2.	How to find the Square Root of 1764?
3.	Is the Square Root of 1764 Rational?
4.	FAQs

What is the Square Root of 1764?

The square root of 1764, (or root 1764), is the number which when multiplied by itself gives the product as 1764. Therefore, the square root of 1764 = √1764 = 42.

☛ Check: Square Root Calculator

How to Find Square Root of 1764?

Square Root of 1764 by Long Division Method

Value of √1764 by Long Division Method

Explanation:

Forming pairs: 17 and 64
Find a number Y (4) such that whose square is <= 17. Now divide 17 by 4 with quotient as 4.
Bring down the next pair 64, to the right of the remainder 1. The new dividend is now 164.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 2) such that 8Z × Z <= 164. After finding Z, together 8 and Z (2) form a new divisor 82 for the new dividend 164.
Divide 164 by 82 with the quotient as 2, giving the remainder = 164 - 82 × 2 = 164 - 164 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 1764 by long division method is 42.

Is Square Root of 1764 Rational?

The value of √1764 is 42. Hence, the square root of 1764 is a rational number.

☛ Also Check:

Square Root of 77 - √77 = 8.77496
Square Root of 12 - √12 = 3.46410
Square Root of 10 - √10 = 3.16228
Square Root of 69 - √69 = 8.30662
Square Root of 92 - √92 = 9.59166
Square Root of 97 - √97 = 9.84886
Square Root of 75 - √75 = 8.66025

Square Root of 1764 Solved Examples

Example 1: Solve the equation x² − 1764 = 0

Solution:

x² - 1764 = 0 i.e. x² = 1764
x = ±√1764
Since the value of the square root of 1764 is 42,
⇒ x = +√1764 or -√1764 = 42 or -42.
Example 2: If the area of an equilateral triangle is 1764√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 1764√3 in²
⇒ a = ±√7056 in
Since length can't be negative,
⇒ a = √7056 = 2 √1764
We know that the square root of 1764 is 42.
⇒ a = 84 in
Example 3: If the surface area of a cube is 10584 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 10584 in²
⇒ a = ±√1764 in
Since length can't be negative,
⇒ a = √1764
We know that the square root of 1764 is 42.
⇒ a = 42 in

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FAQs on the Square Root of 1764

What is the Value of the Square Root of 1764?

The square root of 1764 is 42.

Why is the Square Root of 1764 a Rational Number?

Upon prime factorizing 1764 i.e. 2² × 3² × 7², we find that all the prime factors are in even power. This implies that the square root of 1764 is a positive integer. Therefore, the square root of 1764 is rational.

Is the number 1764 a Perfect Square?

The prime factorization of 1764 = 2² × 3² × 7². Here, all the numbers are in the power of 2. This implies that the square root of 1764 is a positive integer. Therefore, 1764 is a perfect square.

What is the Square of the Square Root of 1764?

The square of the square root of 1764 is the number 1764 itself i.e. (√1764)² = (1764)^2/2 = 1764.

What is the Value of 16 square root 1764?

The square root of 1764 is 42. Therefore, 16 √1764 = 16 × 42 = 672.

Evaluate 18 plus 10 square root 1764

The given expression is 18 + 10 √1764. We know that the square root of 1764 is 42. Therefore, 18 + 10 √1764 = 18 + 10 × 42 = 18 + 420 = 438

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