A day full of math games & activities. Find one near you.

Square Root of 1056

The square root of 1056 is expressed as √1056 in the radical form and as (1056)^½ or (1056)^0.5 in the exponent form. The square root of 1056 rounded up to 6 decimal places is 32.496154. It is the positive solution of the equation x² = 1056. We can express the square root of 1056 in its lowest radical form as 4 √66.

Square Root of 1056: 32.49615361854384
Square Root of 1056 in exponential form: (1056)^½ or (1056)^0.5
Square Root of 1056 in radical form: √1056 or 4 √66

Square Root of 1056

1.	What is the Square Root of 1056?
2.	How to find the Square Root of 1056?
3.	Is the Square Root of 1056 Irrational?
4.	FAQs

What is the Square Root of 1056?

The square root of 1056, (or root 1056), is the number which when multiplied by itself gives the product as 1056. Therefore, the square root of 1056 = √1056 = 4 √66 = 32.49615361854384.

☛ Check: Square Root Calculator

How to Find Square Root of 1056?

Square Root of 1056 by Long Division Method

Value of √1056 by Long Division Method

Explanation:

Forming pairs: 10 and 56
Find a number Y (3) such that whose square is <= 10. Now divide 10 by 3 with quotient as 3.
Bring down the next pair 56, to the right of the remainder 1. The new dividend is now 156.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 2) such that 6Z × Z <= 156. After finding Z, together 6 and Z (2) form a new divisor 62 for the new dividend 156.
Divide 156 by 62 with the quotient as 2, giving the remainder = 156 - 62 × 2 = 156 - 124 = 32.
Now, let's find the decimal places after the quotient 32.
Bring down 00 to the right of this remainder 32. The new dividend is now 3200.
Add the last digit of quotient to divisor i.e. 2 + 62 = 64. To the right of 64, find a digit Z (which is 4) such that 64Z × Z <= 3200. Together they form a new divisor (644) for the new dividend (3200).
Divide 3200 by 644 with the quotient as 4, giving the remainder = 3200 - 644 × 4 = 3200 - 2576 = 624.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1056.

Therefore, the square root of 1056 by long division method is 32.4 approximately.

Is Square Root of 1056 Irrational?

The actual value of √1056 is undetermined. The value of √1056 up to 25 decimal places is 32.49615361854384144183953. Hence, the square root of 1056 is an irrational number.

☛ Also Check:

Square Root of 77 - √77 = 8.77496
Square Root of 192 - √192 = 13.85641
Square Root of 45 - √45 = 6.70820
Square Root of 106 - √106 = 10.29563
Square Root of 65 - √65 = 8.06226
Square Root of 69 - √69 = 8.30662
Square Root of 2 - √2 = 1.41421

Square Root of 1056 Solved Examples

Example 1: Solve the equation x² − 1056 = 0

Solution:

x² - 1056 = 0 i.e. x² = 1056
x = ±√1056
Since the value of the square root of 1056 is 32.496,
⇒ x = +√1056 or -√1056 = 32.496 or -32.496.
Example 2: If the surface area of a cube is 6336 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 = 6336 in²
⇒ a = ±√1056 in
Since length can't be negative,
⇒ a = √1056
We know that the square root of 1056 is 32.496.
⇒ a = 32.496 in
Example 3: If the area of a circle is 1056π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1056π in²
⇒ r = ±√1056 in
Since radius can't be negative,
⇒ r = √1056
The square root of 1056 is 32.496.
⇒ r = 32.496 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 1056

What is the Value of the Square Root of 1056?

The square root of 1056 is 32.49615.

Why is the Square Root of 1056 an Irrational Number?

Upon prime factorizing 1056 i.e. 2⁵ × 3¹ × 11¹, 2 is in odd power. Therefore, the square root of 1056 is irrational.

What is the Square of the Square Root of 1056?

The square of the square root of 1056 is the number 1056 itself i.e. (√1056)² = (1056)^2/2 = 1056.

What is the Square Root of -1056?

The square root of -1056 is an imaginary number. It can be written as √-1056 = √-1 × √1056 = i √1056 = 32.496i
where i = √-1 and it is called the imaginary unit.

Evaluate 20 plus 20 square root 1056

The given expression is 20 + 20 √1056. We know that the square root of 1056 is 32.496. Therefore, 20 + 20 √1056 = 20 + 20 × 32.496 = 20 + 649.923 = 669.923

What is the Square Root of 1056 in Simplest Radical Form?

We need to express 1056 as the product of its prime factors i.e. 1056 = 2 × 2 × 2 × 2 × 2 × 3 × 11. Therefore, √1056 = √2 × 2 × 2 × 2 × 2 × 3 × 11 = 4 √66. Thus, the square root of 1056 in the lowest radical form is 4 √66.

Math worksheets and
visual curriculum