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Square Root of 801

The square root of 801 is expressed as √801 in the radical form and as (801)^½ or (801)^0.5 in the exponent form. The square root of 801 rounded up to 5 decimal places is 28.30194. It is the positive solution of the equation x² = 801. We can express the square root of 801 in its lowest radical form as 3 √89.

Square Root of 801: 28.30194339616981
Square Root of 801 in exponential form: (801)^½ or (801)^0.5
Square Root of 801 in radical form: √801 or 3 √89

Square Root of 801

1.	What is the Square Root of 801?
2.	How to find the Square Root of 801?
3.	Is the Square Root of 801 Irrational?
4.	FAQs

What is the Square Root of 801?

The square root of 801, (or root 801), is the number which when multiplied by itself gives the product as 801. Therefore, the square root of 801 = √801 = 3 √89 = 28.30194339616981.

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How to Find Square Root of 801?

Square Root of 801 by Long Division Method

Value of √801 by Long Division Method

Explanation:

Forming pairs: 08 and 01
Find a number Y (2) such that whose square is <= 8. Now divide 08 by 2 with quotient as 2.
Bring down the next pair 01, to the right of the remainder 4. The new dividend is now 401.
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 8) such that 4Z × Z <= 401. After finding Z, together 4 and Z (8) form a new divisor 48 for the new dividend 401.
Divide 401 by 48 with the quotient as 8, giving the remainder = 401 - 48 × 8 = 401 - 384 = 17.
Now, let's find the decimal places after the quotient 28.
Bring down 00 to the right of this remainder 17. The new dividend is now 1700.
Add the last digit of quotient to divisor i.e. 8 + 48 = 56. To the right of 56, find a digit Z (which is 3) such that 56Z × Z <= 1700. Together they form a new divisor (563) for the new dividend (1700).
Divide 1700 by 563 with the quotient as 3, giving the remainder = 1700 - 563 × 3 = 1700 - 1689 = 11.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 801.

Therefore, the square root of 801 by long division method is 28.3 approximately.

Is Square Root of 801 Irrational?

The actual value of √801 is undetermined. The value of √801 up to 25 decimal places is 28.30194339616981143396198. Hence, the square root of 801 is an irrational number.

☛ Also Check:

Square Root of 2 - √2 = 1.41421
Square Root of 106 - √106 = 10.29563
Square Root of 60 - √60 = 7.74597
Square Root of 33 - √33 = 5.74456
Square Root of 169 - √169 = 13
Square Root of 14 - √14 = 3.74166
Square Root of 22 - √22 = 4.69042

Square Root of 801 Solved Examples

Example 1: Solve the equation x² − 801 = 0

Solution:

x² - 801 = 0 i.e. x² = 801
x = ±√801
Since the value of the square root of 801 is 28.302,
⇒ x = +√801 or -√801 = 28.302 or -28.302.
Example 2: If the area of an equilateral triangle is 801√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 = 801√3 in²
⇒ a = ±√3204 in
Since length can't be negative,
⇒ a = √3204 = 2 √801
We know that the square root of 801 is 28.302.
⇒ a = 56.604 in
Example 3: If the area of a circle is 801π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 801π in²
⇒ r = ±√801 in
Since radius can't be negative,
⇒ r = √801
The square root of 801 is 28.302.
⇒ r = 28.302 in

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FAQs on the Square Root of 801

What is the Value of the Square Root of 801?

The square root of 801 is 28.30194.

Why is the Square Root of 801 an Irrational Number?

Upon prime factorizing 801 i.e. 3² × 89¹, 89 is in odd power. Therefore, the square root of 801 is irrational.

Is the number 801 a Perfect Square?

The prime factorization of 801 = 3² × 89¹. Here, the prime factor 89 is not in the pair. Therefore, 801 is not a perfect square.

What is the Square Root of 801 in Simplest Radical Form?

We need to express 801 as the product of its prime factors i.e. 801 = 3 × 3 × 89. Therefore, √801 = √3 × 3 × 89 = 3 √89. Thus, the square root of 801 in the lowest radical form is 3 √89.

If the Square Root of 801 is 28.302. Find the Value of the Square Root of 8.01.

Let us represent √8.01 in p/q form i.e. √(801/100) = 8.01/10 = 2.830. Hence, the value of √8.01 = 2.830

What is the Square Root of -801?

The square root of -801 is an imaginary number. It can be written as √-801 = √-1 × √801 = i √801 = 28.301i
where i = √-1 and it is called the imaginary unit.

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