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Square Root of 1762

The square root of 1762 is expressed as √1762 in the radical form and as (1762)^½ or (1762)^0.5 in the exponent form. The square root of 1762 rounded up to 6 decimal places is 41.976184. It is the positive solution of the equation x² = 1762.

Square Root of 1762: 41.97618372363071
Square Root of 1762 in exponential form: (1762)^½ or (1762)^0.5
Square Root of 1762 in radical form: √1762

Square Root of 1762

1.	What is the Square Root of 1762?
2.	How to find the Square Root of 1762?
3.	Is the Square Root of 1762 Irrational?
4.	FAQs

What is the Square Root of 1762?

The square root of 1762, (or root 1762), is the number which when multiplied by itself gives the product as 1762. Therefore, the square root of 1762 = √1762 = 41.97618372363071.

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How to Find Square Root of 1762?

Square Root of 1762 by Long Division Method

Value of √1762 by Long Division Method

Explanation:

Forming pairs: 17 and 62
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 62, to the right of the remainder 1. The new dividend is now 162.
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 1) such that 8Z × Z <= 162. After finding Z, together 8 and Z (1) form a new divisor 81 for the new dividend 162.
Divide 162 by 81 with the quotient as 1, giving the remainder = 162 - 81 × 1 = 162 - 81 = 81.
Now, let's find the decimal places after the quotient 41.
Bring down 00 to the right of this remainder 81. The new dividend is now 8100.
Add the last digit of quotient to divisor i.e. 1 + 81 = 82. To the right of 82, find a digit Z (which is 9) such that 82Z × Z <= 8100. Together they form a new divisor (829) for the new dividend (8100).
Divide 8100 by 829 with the quotient as 9, giving the remainder = 8100 - 829 × 9 = 8100 - 7461 = 639.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1762.

Therefore, the square root of 1762 by long division method is 41.9 approx.

Is Square Root of 1762 Irrational?

The actual value of √1762 is undetermined. The value of √1762 up to 25 decimal places is 41.97618372363071311603762. Hence, the square root of 1762 is an irrational number.

☛ Also Check:

Square Root of 729 - √729 = 27
Square Root of 30 - √30 = 5.47723
Square Root of 125 - √125 = 11.18034
Square Root of 33 - √33 = 5.74456
Square Root of 69 - √69 = 8.30662
Square Root of 109 - √109 = 10.44031
Square Root of 25 - √25 = 5

Square Root of 1762 Solved Examples

Example 1: Solve the equation x² − 1762 = 0

Solution:

x² - 1762 = 0 i.e. x² = 1762
x = ±√1762
Since the value of the square root of 1762 is 41.976,
⇒ x = +√1762 or -√1762 = 41.976 or -41.976.
Example 2: If the surface area of a sphere is 7048π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 7048π in²
⇒ r = ±√1762 in
Since radius can't be negative,
⇒ r = √1762
The square root of 1762 is 41.976.
⇒ r = 41.976 in
Example 3: If the surface area of a cube is 10572 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 = 10572 in²
⇒ a = ±√1762 in
Since length can't be negative,
⇒ a = √1762
We know that the square root of 1762 is 41.976.
⇒ a = 41.976 in

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FAQs on the Square Root of 1762

What is the Value of the Square Root of 1762?

The square root of 1762 is 41.97618.

Why is the Square Root of 1762 an Irrational Number?

Upon prime factorizing 1762 i.e. 2¹ × 881¹, 2 is in odd power. Therefore, the square root of 1762 is irrational.

What is the Value of 6 square root 1762?

The square root of 1762 is 41.976. Therefore, 6 √1762 = 6 × 41.976 = 251.857.

What is the Square Root of 1762 in Simplest Radical Form?

We need to express 1762 as the product of its prime factors i.e. 1762 = 2 × 881. Therefore, as visible, the radical form of the square root of 1762 cannot be simplified further. Therefore, the simplest radical form of the square root of 1762 can be written as √1762

Evaluate 15 plus 10 square root 1762

The given expression is 15 + 10 √1762. We know that the square root of 1762 is 41.976. Therefore, 15 + 10 √1762 = 15 + 10 × 41.976 = 15 + 419.762 = 434.762

What is the Square Root of -1762?

The square root of -1762 is an imaginary number. It can be written as √-1762 = √-1 × √1762 = i √1762 = 41.976i
where i = √-1 and it is called the imaginary unit.

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