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Square Root of 1750

The square root of 1750 is expressed as √1750 in the radical form and as (1750)^½ or (1750)^0.5 in the exponent form. The square root of 1750 rounded up to 8 decimal places is 41.83300133. It is the positive solution of the equation x² = 1750. We can express the square root of 1750 in its lowest radical form as 5 √70.

Square Root of 1750: 41.83300132670378
Square Root of 1750 in exponential form: (1750)^½ or (1750)^0.5
Square Root of 1750 in radical form: √1750 or 5 √70

Square Root of 1750

1.	What is the Square Root of 1750?
2.	How to find the Square Root of 1750?
3.	Is the Square Root of 1750 Irrational?
4.	FAQs

What is the Square Root of 1750?

The square root of 1750, (or root 1750), is the number which when multiplied by itself gives the product as 1750. Therefore, the square root of 1750 = √1750 = 5 √70 = 41.83300132670378.

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How to Find Square Root of 1750?

Square Root of 1750 by Long Division Method

Value of √1750 by Long Division Method

Explanation:

Forming pairs: 17 and 50
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 50, to the right of the remainder 1. The new dividend is now 150.
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 <= 150. After finding Z, together 8 and Z (1) form a new divisor 81 for the new dividend 150.
Divide 150 by 81 with the quotient as 1, giving the remainder = 150 - 81 × 1 = 150 - 81 = 69.
Now, let's find the decimal places after the quotient 41.
Bring down 00 to the right of this remainder 69. The new dividend is now 6900.
Add the last digit of quotient to divisor i.e. 1 + 81 = 82. To the right of 82, find a digit Z (which is 8) such that 82Z × Z <= 6900. Together they form a new divisor (828) for the new dividend (6900).
Divide 6900 by 828 with the quotient as 8, giving the remainder = 6900 - 828 × 8 = 6900 - 6624 = 276.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1750.

Therefore, the square root of 1750 by long division method is 41.8 approx.

Is Square Root of 1750 Irrational?

The actual value of √1750 is undetermined. The value of √1750 up to 25 decimal places is 41.83300132670377739890860. Hence, the square root of 1750 is an irrational number.

☛ Also Check:

Square Root of 42 - √42 = 6.48074
Square Root of 54 - √54 = 7.34847
Square Root of 169 - √169 = 13
Square Root of 1024 - √1024 = 32
Square Root of 12 - √12 = 3.46410
Square Root of 15 - √15 = 3.87298
Square Root of 21 - √21 = 4.58258

Square Root of 1750 Solved Examples

Example 1: Solve the equation x² − 1750 = 0

Solution:

x² - 1750 = 0 i.e. x² = 1750
x = ±√1750
Since the value of the square root of 1750 is 41.833,
⇒ x = +√1750 or -√1750 = 41.833 or -41.833.
Example 2: If the area of a circle is 1750π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1750π in²
⇒ r = ±√1750 in
Since radius can't be negative,
⇒ r = √1750
The square root of 1750 is 41.833.
⇒ r = 41.833 in
Example 3: If the area of a square is 1750 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 = 1750 in²
⇒ a = ±√1750 in
Since length can't be negative,
⇒ a = √1750 = 41.833 in

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FAQs on the Square Root of 1750

What is the Value of the Square Root of 1750?

The square root of 1750 is 41.833.

Why is the Square Root of 1750 an Irrational Number?

Upon prime factorizing 1750 i.e. 2¹ × 5³ × 7¹, 2 is in odd power. Therefore, the square root of 1750 is irrational.

Evaluate 6 plus 15 square root 1750

The given expression is 6 + 15 √1750. We know that the square root of 1750 is 41.833. Therefore, 6 + 15 √1750 = 6 + 15 × 41.833 = 6 + 627.495 = 633.495

What is the Square Root of -1750?

The square root of -1750 is an imaginary number. It can be written as √-1750 = √-1 × √1750 = i √1750 = 41.833i
where i = √-1 and it is called the imaginary unit.

What is the Value of 6 square root 1750?

The square root of 1750 is 41.833. Therefore, 6 √1750 = 6 × 41.833 = 250.998.

What is the Square Root of 1750 in Simplest Radical Form?

We need to express 1750 as the product of its prime factors i.e. 1750 = 2 × 5 × 5 × 5 × 7. Therefore, √1750 = √2 × 5 × 5 × 5 × 7 = 5 √70. Thus, the square root of 1750 in the lowest radical form is 5 √70.

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