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Square Root of 304

The square root of 304 is expressed as √304 in the radical form and as (304)^½ or (304)^0.5 in the exponent form. The square root of 304 rounded up to 8 decimal places is 17.43559577. It is the positive solution of the equation x² = 304. We can express the square root of 304 in its lowest radical form as 4 √19.

Square Root of 304: 17.435595774162696
Square Root of 304 in exponential form: (304)^½ or (304)^0.5
Square Root of 304 in radical form: √304 or 4 √19

Square Root of 304

1.	What is the Square Root of 304?
2.	How to find the Square Root of 304?
3.	Is the Square Root of 304 Irrational?
4.	FAQs

What is the Square Root of 304?

The square root of 304, (or root 304), is the number which when multiplied by itself gives the product as 304. Therefore, the square root of 304 = √304 = 4 √19 = 17.435595774162696.

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How to Find Square Root of 304?

Square Root of 304 by Long Division Method

Value of √304 by Long Division Method

Explanation:

Forming pairs: 03 and 04
Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
Bring down the next pair 04, to the right of the remainder 2. The new dividend is now 204.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 7) such that 2Z × Z <= 204. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 204.
Divide 204 by 27 with the quotient as 7, giving the remainder = 204 - 27 × 7 = 204 - 189 = 15.
Now, let's find the decimal places after the quotient 17.
Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
Add the last digit of quotient to divisor i.e. 7 + 27 = 34. To the right of 34, find a digit Z (which is 4) such that 34Z × Z <= 1500. Together they form a new divisor (344) for the new dividend (1500).
Divide 1500 by 344 with the quotient as 4, giving the remainder = 1500 - 344 × 4 = 1500 - 1376 = 124.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 304.

Therefore, the square root of 304 by long division method is 17.4 approx.

Is Square Root of 304 Irrational?

The actual value of √304 is undetermined. The value of √304 up to 25 decimal places is 17.43559577416269420894793. Hence, the square root of 304 is an irrational number.

☛ Also Check:

Square Root of 729 - √729 = 27
Square Root of 25 - √25 = 5
Square Root of 106 - √106 = 10.29563
Square Root of 92 - √92 = 9.59166
Square Root of 52 - √52 = 7.21110
Square Root of 35 - √35 = 5.91608
Square Root of 113 - √113 = 10.63015

Square Root of 304 Solved Examples

Example 1: Solve the equation x² − 304 = 0

Solution:

x² - 304 = 0 i.e. x² = 304
x = ±√304
Since the value of the square root of 304 is 17.436,
⇒ x = +√304 or -√304 = 17.436 or -17.436.
Example 2: If the area of a circle is 304π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 304π in²
⇒ r = ±√304 in
Since radius can't be negative,
⇒ r = √304
The square root of 304 is 17.436.
⇒ r = 17.436 in
Example 3: If the surface area of a sphere is 1216π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1216π in²
⇒ r = ±√304 in
Since radius can't be negative,
⇒ r = √304
The square root of 304 is 17.436.
⇒ r = 17.436 in

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FAQs on the Square Root of 304

What is the Value of the Square Root of 304?

The square root of 304 is 17.43559.

Why is the Square Root of 304 an Irrational Number?

Upon prime factorizing 304 i.e. 2⁴ × 19¹, 19 is in odd power. Therefore, the square root of 304 is irrational.

Is the number 304 a Perfect Square?

The prime factorization of 304 = 2⁴ × 19¹. Here, the prime factor 19 is not in the pair. Therefore, 304 is not a perfect square.

If the Square Root of 304 is 17.436. Find the Value of the Square Root of 3.04.

Let us represent √3.04 in p/q form i.e. √(304/100) = 3.04/10 = 1.744. Hence, the value of √3.04 = 1.744

What is the Value of 17 square root 304?

The square root of 304 is 17.436. Therefore, 17 √304 = 17 × 17.436 = 296.405.

What is the Square Root of 304 in Simplest Radical Form?

We need to express 304 as the product of its prime factors i.e. 304 = 2 × 2 × 2 × 2 × 19. Therefore, √304 = √2 × 2 × 2 × 2 × 19 = 4 √19. Thus, the square root of 304 in the lowest radical form is 4 √19.

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