A day full of math games & activities. Find one near you.

Square Root of 575

The square root of 575 is expressed as √575 in the radical form and as (575)^½ or (575)^0.5 in the exponent form. The square root of 575 rounded up to 7 decimal places is 23.9791576. It is the positive solution of the equation x² = 575. We can express the square root of 575 in its lowest radical form as 5 √23.

Square Root of 575: 23.979157616563597
Square Root of 575 in exponential form: (575)^½ or (575)^0.5
Square Root of 575 in radical form: √575 or 5 √23

Square Root of 575

1.	What is the Square Root of 575?
2.	How to find the Square Root of 575?
3.	Is the Square Root of 575 Irrational?
4.	FAQs

What is the Square Root of 575?

The square root of 575, (or root 575), is the number which when multiplied by itself gives the product as 575. Therefore, the square root of 575 = √575 = 5 √23 = 23.979157616563597.

☛ Check: Square Root Calculator

How to Find Square Root of 575?

Square Root of 575 by Long Division Method

Value of √575 by Long Division Method

Explanation:

Forming pairs: 05 and 75
Find a number Y (2) such that whose square is <= 5. Now divide 05 by 2 with quotient as 2.
Bring down the next pair 75, to the right of the remainder 1. The new dividend is now 175.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 3) such that 4Z × Z <= 175. After finding Z, together 4 and Z (3) form a new divisor 43 for the new dividend 175.
Divide 175 by 43 with the quotient as 3, giving the remainder = 175 - 43 × 3 = 175 - 129 = 46.
Now, let's find the decimal places after the quotient 23.
Bring down 00 to the right of this remainder 46. The new dividend is now 4600.
Add the last digit of quotient to divisor i.e. 3 + 43 = 46. To the right of 46, find a digit Z (which is 9) such that 46Z × Z <= 4600. Together they form a new divisor (469) for the new dividend (4600).
Divide 4600 by 469 with the quotient as 9, giving the remainder = 4600 - 469 × 9 = 4600 - 4221 = 379.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 575.

Therefore, the square root of 575 by long division method is 23.9 approx.

Is Square Root of 575 Irrational?

The actual value of √575 is undetermined. The value of √575 up to 25 decimal places is 23.97915761656359770798719. Hence, the square root of 575 is an irrational number.

☛ Also Check:

Square Root of 400 - √400 = 20
Square Root of 105 - √105 = 10.24695
Square Root of 30 - √30 = 5.47723
Square Root of 56 - √56 = 7.48331
Square Root of 2 - √2 = 1.41421
Square Root of 89 - √89 = 9.43398
Square Root of 42 - √42 = 6.48074

Square Root of 575 Solved Examples

Example 1: Solve the equation x² − 575 = 0

Solution:

x² - 575 = 0 i.e. x² = 575
x = ±√575
Since the value of the square root of 575 is 23.979,
⇒ x = +√575 or -√575 = 23.979 or -23.979.
Example 2: If the surface area of a sphere is 2300π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2300π in²
⇒ r = ±√575 in
Since radius can't be negative,
⇒ r = √575
The square root of 575 is 23.979.
⇒ r = 23.979 in
Example 3: If the area of a square is 575 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 = 575 in²
⇒ a = ±√575 in
Since length can't be negative,
⇒ a = √575 = 23.979 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 575

What is the Value of the Square Root of 575?

The square root of 575 is 23.97915.

Why is the Square Root of 575 an Irrational Number?

Upon prime factorizing 575 i.e. 5² × 23¹, 23 is in odd power. Therefore, the square root of 575 is irrational.

What is the Square Root of 575 in Simplest Radical Form?

We need to express 575 as the product of its prime factors i.e. 575 = 5 × 5 × 23. Therefore, √575 = √5 × 5 × 23 = 5 √23. Thus, the square root of 575 in the lowest radical form is 5 √23.

Is the number 575 a Perfect Square?

The prime factorization of 575 = 5² × 23¹. Here, the prime factor 23 is not in the pair. Therefore, 575 is not a perfect square.

What is the Square of the Square Root of 575?

The square of the square root of 575 is the number 575 itself i.e. (√575)² = (575)^2/2 = 575.

What is the Square Root of -575?

The square root of -575 is an imaginary number. It can be written as √-575 = √-1 × √575 = i √575 = 23.979i
where i = √-1 and it is called the imaginary unit.

Math worksheets and
visual curriculum