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Square Root of 375

The square root of 375 is expressed as √375 in the radical form and as (375)^½ or (375)^0.5 in the exponent form. The square root of 375 rounded up to 6 decimal places is 19.364917. It is the positive solution of the equation x² = 375. We can express the square root of 375 in its lowest radical form as 5 √15.

Square Root of 375: 19.364916731037084
Square Root of 375 in exponential form: (375)^½ or (375)^0.5
Square Root of 375 in radical form: √375 or 5 √15

Square Root of 375

1.	What is the Square Root of 375?
2.	How to find the Square Root of 375?
3.	Is the Square Root of 375 Irrational?
4.	FAQs

What is the Square Root of 375?

The square root of 375, (or root 375), is the number which when multiplied by itself gives the product as 375. Therefore, the square root of 375 = √375 = 5 √15 = 19.364916731037084.

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How to Find Square Root of 375?

Square Root of 375 by Long Division Method

Value of √375 by Long Division Method

Explanation:

Forming pairs: 03 and 75
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 75, to the right of the remainder 2. The new dividend is now 275.
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 9) such that 2Z × Z <= 275. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 275.
Divide 275 by 29 with the quotient as 9, giving the remainder = 275 - 29 × 9 = 275 - 261 = 14.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 14. The new dividend is now 1400.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 3) such that 38Z × Z <= 1400. Together they form a new divisor (383) for the new dividend (1400).
Divide 1400 by 383 with the quotient as 3, giving the remainder = 1400 - 383 × 3 = 1400 - 1149 = 251.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 375.

Therefore, the square root of 375 by long division method is 19.3 approximately.

Is Square Root of 375 Irrational?

The actual value of √375 is undetermined. The value of √375 up to 25 decimal places is 19.36491673103708442589633. Hence, the square root of 375 is an irrational number.

☛ Also Check:

Square Root of 75 - √75 = 8.66025
Square Root of 125 - √125 = 11.18034
Square Root of 15 - √15 = 3.87298
Square Root of 100 - √100 = 10
Square Root of 98 - √98 = 9.89949
Square Root of 21 - √21 = 4.58258
Square Root of 80 - √80 = 8.94427

Square Root of 375 Solved Examples

Example 1: Solve the equation x² − 375 = 0

Solution:

x² - 375 = 0 i.e. x² = 375
x = ±√375
Since the value of the square root of 375 is 19.365,
⇒ x = +√375 or -√375 = 19.365 or -19.365.
Example 2: If the surface area of a sphere is 1500π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1500π in²
⇒ r = ±√375 in
Since radius can't be negative,
⇒ r = √375
The square root of 375 is 19.365.
⇒ r = 19.365 in
Example 3: If the surface area of a cube is 2250 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 2250 in²
⇒ a = ±√375 in
Since length can't be negative,
⇒ a = √375
We know that the square root of 375 is 19.365.
⇒ a = 19.365 in

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FAQs on the Square Root of 375

What is the Value of the Square Root of 375?

The square root of 375 is 19.36491.

Why is the Square Root of 375 an Irrational Number?

Upon prime factorizing 375 i.e. 3¹ × 5³, 3 is in odd power. Therefore, the square root of 375 is irrational.

What is the Square Root of 375 in Simplest Radical Form?

We need to express 375 as the product of its prime factors i.e. 375 = 3 × 5 × 5 × 5. Therefore, √375 = √3 × 5 × 5 × 5 = 5 √15. Thus, the square root of 375 in the lowest radical form is 5 √15.

Is the number 375 a Perfect Square?

The prime factorization of 375 = 3¹ × 5³. Here, the prime factor 3 is not in the pair. Therefore, 375 is not a perfect square.

Evaluate 5 plus 16 square root 375

The given expression is 5 + 16 √375. We know that the square root of 375 is 19.365. Therefore, 5 + 16 √375 = 5 + 16 × 19.365 = 5 + 309.839 = 314.839

What is the Square Root of -375?

The square root of -375 is an imaginary number. It can be written as √-375 = √-1 × √375 = i √375 = 19.364i
where i = √-1 and it is called the imaginary unit.

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