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Square Root of 1440

The square root of 1440 is expressed as √1440 in the radical form and as (1440)^½ or (1440)^0.5 in the exponent form. The square root of 1440 rounded up to 6 decimal places is 37.947332. It is the positive solution of the equation x² = 1440. We can express the square root of 1440 in its lowest radical form as 12 √10.

Square Root of 1440: 37.94733192202055
Square Root of 1440 in exponential form: (1440)^½ or (1440)^0.5
Square Root of 1440 in radical form: √1440 or 12 √10

Square Root of 1440

1.	What is the Square Root of 1440?
2.	How to find the Square Root of 1440?
3.	Is the Square Root of 1440 Irrational?
4.	FAQs

What is the Square Root of 1440?

The square root of 1440, (or root 1440), is the number which when multiplied by itself gives the product as 1440. Therefore, the square root of 1440 = √1440 = 12 √10 = 37.94733192202055.

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How to Find Square Root of 1440?

Square Root of 1440 by Long Division Method

Value of √1440 by Long Division Method

Explanation:

Forming pairs: 14 and 40
Find a number Y (3) such that whose square is <= 14. Now divide 14 by 3 with quotient as 3.
Bring down the next pair 40, to the right of the remainder 5. The new dividend is now 540.
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 7) such that 6Z × Z <= 540. After finding Z, together 6 and Z (7) form a new divisor 67 for the new dividend 540.
Divide 540 by 67 with the quotient as 7, giving the remainder = 540 - 67 × 7 = 540 - 469 = 71.
Now, let's find the decimal places after the quotient 37.
Bring down 00 to the right of this remainder 71. The new dividend is now 7100.
Add the last digit of quotient to divisor i.e. 7 + 67 = 74. To the right of 74, find a digit Z (which is 9) such that 74Z × Z <= 7100. Together they form a new divisor (749) for the new dividend (7100).
Divide 7100 by 749 with the quotient as 9, giving the remainder = 7100 - 749 × 9 = 7100 - 6741 = 359.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1440.

Therefore, the square root of 1440 by long division method is 37.9 approx.

Is Square Root of 1440 Irrational?

The actual value of √1440 is undetermined. The value of √1440 up to 25 decimal places is 37.94733192202055198398672. Hence, the square root of 1440 is an irrational number.

☛ Also Check:

Square Root of 125 - √125 = 11.18034
Square Root of 109 - √109 = 10.44031
Square Root of 60 - √60 = 7.74597
Square Root of 15 - √15 = 3.87298
Square Root of 34 - √34 = 5.83095
Square Root of 136 - √136 = 11.66190
Square Root of 192 - √192 = 13.85641

Square Root of 1440 Solved Examples

Example 1: Solve the equation x² − 1440 = 0

Solution:

x² - 1440 = 0 i.e. x² = 1440
x = ±√1440
Since the value of the square root of 1440 is 37.947,
⇒ x = +√1440 or -√1440 = 37.947 or -37.947.
Example 2: If the area of a square is 1440 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 1440 in²
⇒ a = ±√1440 in
Since length can't be negative,
⇒ a = √1440 = 37.947 in
Example 3: If the surface area of a cube is 8640 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 = 8640 in²
⇒ a = ±√1440 in
Since length can't be negative,
⇒ a = √1440
We know that the square root of 1440 is 37.947.
⇒ a = 37.947 in

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FAQs on the Square Root of 1440

What is the Value of the Square Root of 1440?

The square root of 1440 is 37.94733.

Why is the Square Root of 1440 an Irrational Number?

Upon prime factorizing 1440 i.e. 2⁵ × 3² × 5¹, 2 is in odd power. Therefore, the square root of 1440 is irrational.

What is the Square of the Square Root of 1440?

The square of the square root of 1440 is the number 1440 itself i.e. (√1440)² = (1440)^2/2 = 1440.

Is the number 1440 a Perfect Square?

The prime factorization of 1440 = 2⁵ × 3² × 5¹. Here, the prime factor 2 is not in the pair. Therefore, 1440 is not a perfect square.

Evaluate 5 plus 4 square root 1440

The given expression is 5 + 4 √1440. We know that the square root of 1440 is 37.947. Therefore, 5 + 4 √1440 = 5 + 4 × 37.947 = 5 + 151.789 = 156.789

What is the Square Root of -1440?

The square root of -1440 is an imaginary number. It can be written as √-1440 = √-1 × √1440 = i √1440 = 37.947i
where i = √-1 and it is called the imaginary unit.

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