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Square Root of 1620

The square root of 1620 is expressed as √1620 in the radical form and as (1620)^½ or (1620)^0.5 in the exponent form. The square root of 1620 rounded up to 7 decimal places is 40.2492236. It is the positive solution of the equation x² = 1620. We can express the square root of 1620 in its lowest radical form as 18 √5.

Square Root of 1620: 40.24922359499622
Square Root of 1620 in exponential form: (1620)^½ or (1620)^0.5
Square Root of 1620 in radical form: √1620 or 18 √5

Square Root of 1620

1.	What is the Square Root of 1620?
2.	How to find the Square Root of 1620?
3.	Is the Square Root of 1620 Irrational?
4.	FAQs

What is the Square Root of 1620?

The square root of 1620, (or root 1620), is the number which when multiplied by itself gives the product as 1620. Therefore, the square root of 1620 = √1620 = 18 √5 = 40.24922359499622.

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How to Find Square Root of 1620?

Square Root of 1620 by Long Division Method

Value of √1620 by Long Division Method

Explanation:

Forming pairs: 16 and 20
Find a number Y (4) such that whose square is <= 16. Now divide 16 by 4 with quotient as 4.
Bring down the next pair 20, to the right of the remainder 0. The new dividend is now 20.
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 0) such that 8Z × Z <= 20. After finding Z, together 8 and Z (0) form a new divisor 80 for the new dividend 20.
Divide 20 by 80 with the quotient as 0, giving the remainder = 20 - 80 × 0 = 20 - 0 = 20.
Now, let's find the decimal places after the quotient 40.
Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
Add the last digit of quotient to divisor i.e. 0 + 80 = 80. To the right of 80, find a digit Z (which is 2) such that 80Z × Z <= 2000. Together they form a new divisor (802) for the new dividend (2000).
Divide 2000 by 802 with the quotient as 2, giving the remainder = 2000 - 802 × 2 = 2000 - 1604 = 396.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1620.

Therefore, the square root of 1620 by long division method is 40.2 approx.

Is Square Root of 1620 Irrational?

The actual value of √1620 is undetermined. The value of √1620 up to 25 decimal places is 40.24922359499621453536513. Hence, the square root of 1620 is an irrational number.

☛ Also Check:

Square Root of 80 - √80 = 8.94427
Square Root of 77 - √77 = 8.77496
Square Root of 51 - √51 = 7.14143
Square Root of 25 - √25 = 5
Square Root of 73 - √73 = 8.54400
Square Root of 225 - √225 = 15
Square Root of 45 - √45 = 6.70820

Square Root of 1620 Solved Examples

Example 1: Solve the equation x² − 1620 = 0

Solution:

x² - 1620 = 0 i.e. x² = 1620
x = ±√1620
Since the value of the square root of 1620 is 40.249,
⇒ x = +√1620 or -√1620 = 40.249 or -40.249.
Example 2: If the surface area of a cube is 9720 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 = 9720 in²
⇒ a = ±√1620 in
Since length can't be negative,
⇒ a = √1620
We know that the square root of 1620 is 40.249.
⇒ a = 40.249 in
Example 3: If the area of a square is 1620 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 = 1620 in²
⇒ a = ±√1620 in
Since length can't be negative,
⇒ a = √1620 = 40.249 in

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FAQs on the Square Root of 1620

What is the Value of the Square Root of 1620?

The square root of 1620 is 40.24922.

Why is the Square Root of 1620 an Irrational Number?

Upon prime factorizing 1620 i.e. 2² × 3⁴ × 5¹, 5 is in odd power. Therefore, the square root of 1620 is irrational.

What is the Square Root of 1620 in Simplest Radical Form?

We need to express 1620 as the product of its prime factors i.e. 1620 = 2 × 2 × 3 × 3 × 3 × 3 × 5. Therefore, √1620 = √2 × 2 × 3 × 3 × 3 × 3 × 5 = 18 √5. Thus, the square root of 1620 in the lowest radical form is 18 √5.

If the Square Root of 1620 is 40.249. Find the Value of the Square Root of 16.2.

Let us represent √16.2 in p/q form i.e. √(1620/100) = 16.2/10 = 4.025. Hence, the value of √16.2 = 4.025

What is the Value of 17 square root 1620?

The square root of 1620 is 40.249. Therefore, 17 √1620 = 17 × 40.249 = 684.237.

What is the Square Root of -1620?

The square root of -1620 is an imaginary number. It can be written as √-1620 = √-1 × √1620 = i √1620 = 40.249i
where i = √-1 and it is called the imaginary unit.

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