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Square Root of 1700

The square root of 1700 is expressed as √1700 in the radical form and as (1700)^½ or (1700)^0.5 in the exponent form. The square root of 1700 rounded up to 5 decimal places is 41.23106. It is the positive solution of the equation x² = 1700. We can express the square root of 1700 in its lowest radical form as 10 √17.

Square Root of 1700: 41.23105625617661
Square Root of 1700 in exponential form: (1700)^½ or (1700)^0.5
Square Root of 1700 in radical form: √1700 or 10 √17

Square Root of 1700

1.	What is the Square Root of 1700?
2.	How to find the Square Root of 1700?
3.	Is the Square Root of 1700 Irrational?
4.	FAQs

What is the Square Root of 1700?

The square root of 1700, (or root 1700), is the number which when multiplied by itself gives the product as 1700. Therefore, the square root of 1700 = √1700 = 10 √17 = 41.23105625617661.

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How to Find Square Root of 1700?

Square Root of 1700 by Long Division Method

Value of √1700 by Long Division Method

Explanation:

Forming pairs: 17 and 00
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 00, to the right of the remainder 1. The new dividend is now 100.
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 <= 100. After finding Z, together 8 and Z (1) form a new divisor 81 for the new dividend 100.
Divide 100 by 81 with the quotient as 1, giving the remainder = 100 - 81 × 1 = 100 - 81 = 19.
Now, let's find the decimal places after the quotient 41.
Bring down 00 to the right of this remainder 19. The new dividend is now 1900.
Add the last digit of quotient to divisor i.e. 1 + 81 = 82. To the right of 82, find a digit Z (which is 2) such that 82Z × Z <= 1900. Together they form a new divisor (822) for the new dividend (1900).
Divide 1900 by 822 with the quotient as 2, giving the remainder = 1900 - 822 × 2 = 1900 - 1644 = 256.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1700.

Therefore, the square root of 1700 by long division method is 41.2 approximately.

Is Square Root of 1700 Irrational?

The actual value of √1700 is undetermined. The value of √1700 up to 25 decimal places is 41.23105625617660549821410. Hence, the square root of 1700 is an irrational number.

☛ Also Check:

Square Root of 14 - √14 = 3.74166
Square Root of 73 - √73 = 8.54400
Square Root of 169 - √169 = 13
Square Root of 96 - √96 = 9.79796
Square Root of 63 - √63 = 7.93725
Square Root of 77 - √77 = 8.77496
Square Root of 90 - √90 = 9.48683

Square Root of 1700 Solved Examples

Example 1: Solve the equation x² − 1700 = 0

Solution:

x² - 1700 = 0 i.e. x² = 1700
x = ±√1700
Since the value of the square root of 1700 is 41.231,
⇒ x = +√1700 or -√1700 = 41.231 or -41.231.
Example 2: If the area of an equilateral triangle is 1700√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 1700√3 in²
⇒ a = ±√6800 in
Since length can't be negative,
⇒ a = √6800 = 2 √1700
We know that the square root of 1700 is 41.231.
⇒ a = 82.462 in
Example 3: If the area of a square is 1700 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 = 1700 in²
⇒ a = ±√1700 in
Since length can't be negative,
⇒ a = √1700 = 41.231 in

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FAQs on the Square Root of 1700

What is the Value of the Square Root of 1700?

The square root of 1700 is 41.23105.

Why is the Square Root of 1700 an Irrational Number?

Upon prime factorizing 1700 i.e. 2² × 5² × 17¹, 17 is in odd power. Therefore, the square root of 1700 is irrational.

Is the number 1700 a Perfect Square?

The prime factorization of 1700 = 2² × 5² × 17¹. Here, the prime factor 17 is not in the pair. Therefore, 1700 is not a perfect square.

What is the Square Root of -1700?

The square root of -1700 is an imaginary number. It can be written as √-1700 = √-1 × √1700 = i √1700 = 41.231i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1700?

The square of the square root of 1700 is the number 1700 itself i.e. (√1700)² = (1700)^2/2 = 1700.

What is the Square Root of 1700 in Simplest Radical Form?

We need to express 1700 as the product of its prime factors i.e. 1700 = 2 × 2 × 5 × 5 × 17. Therefore, √1700 = √2 × 2 × 5 × 5 × 17 = 10 √17. Thus, the square root of 1700 in the lowest radical form is 10 √17.

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