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Square Root of 378

The square root of 378 is expressed as √378 in the radical form and as (378)^½ or (378)^0.5 in the exponent form. The square root of 378 rounded up to 8 decimal places is 19.44222210. It is the positive solution of the equation x² = 378. We can express the square root of 378 in its lowest radical form as 3 √42.

Square Root of 378: 19.44222209522358
Square Root of 378 in exponential form: (378)^½ or (378)^0.5
Square Root of 378 in radical form: √378 or 3 √42

Square Root of 378

1.	What is the Square Root of 378?
2.	How to find the Square Root of 378?
3.	Is the Square Root of 378 Irrational?
4.	FAQs

What is the Square Root of 378?

The square root of 378, (or root 378), is the number which when multiplied by itself gives the product as 378. Therefore, the square root of 378 = √378 = 3 √42 = 19.44222209522358.

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How to Find Square Root of 378?

Square Root of 378 by Long Division Method

Value of √378 by Long Division Method

Explanation:

Forming pairs: 03 and 78
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 78, to the right of the remainder 2. The new dividend is now 278.
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 <= 278. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 278.
Divide 278 by 29 with the quotient as 9, giving the remainder = 278 - 29 × 9 = 278 - 261 = 17.
Now, let's find the decimal places after the quotient 19.
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. 9 + 29 = 38. To the right of 38, find a digit Z (which is 4) such that 38Z × Z <= 1700. Together they form a new divisor (384) for the new dividend (1700).
Divide 1700 by 384 with the quotient as 4, giving the remainder = 1700 - 384 × 4 = 1700 - 1536 = 164.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 378.

Therefore, the square root of 378 by long division method is 19.4 approximately.

Is Square Root of 378 Irrational?

The actual value of √378 is undetermined. The value of √378 up to 25 decimal places is 19.44222209522358069289790. Hence, the square root of 378 is an irrational number.

☛ Also Check:

Square Root of 729 - √729 = 27
Square Root of 113 - √113 = 10.63015
Square Root of 42 - √42 = 6.48074
Square Root of 29 - √29 = 5.38516
Square Root of 40 - √40 = 6.32456
Square Root of 61 - √61 = 7.81025
Square Root of 162 - √162 = 12.72792

Square Root of 378 Solved Examples

Example 1: Solve the equation x² − 378 = 0

Solution:

x² - 378 = 0 i.e. x² = 378
x = ±√378
Since the value of the square root of 378 is 19.442,
⇒ x = +√378 or -√378 = 19.442 or -19.442.
Example 2: If the area of a circle is 378π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 378π in²
⇒ r = ±√378 in
Since radius can't be negative,
⇒ r = √378
The square root of 378 is 19.442.
⇒ r = 19.442 in
Example 3: If the area of an equilateral triangle is 378√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 = 378√3 in²
⇒ a = ±√1512 in
Since length can't be negative,
⇒ a = √1512 = 2 √378
We know that the square root of 378 is 19.442.
⇒ a = 38.884 in

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FAQs on the Square Root of 378

What is the Value of the Square Root of 378?

The square root of 378 is 19.44222.

Why is the Square Root of 378 an Irrational Number?

Upon prime factorizing 378 i.e. 2¹ × 3³ × 7¹, 2 is in odd power. Therefore, the square root of 378 is irrational.

If the Square Root of 378 is 19.442. Find the Value of the Square Root of 3.78.

Let us represent √3.78 in p/q form i.e. √(378/100) = 3.78/10 = 1.944. Hence, the value of √3.78 = 1.944

What is the Square Root of 378 in Simplest Radical Form?

We need to express 378 as the product of its prime factors i.e. 378 = 2 × 3 × 3 × 3 × 7. Therefore, √378 = √2 × 3 × 3 × 3 × 7 = 3 √42. Thus, the square root of 378 in the lowest radical form is 3 √42.

Evaluate 4 plus 8 square root 378

The given expression is 4 + 8 √378. We know that the square root of 378 is 19.442. Therefore, 4 + 8 √378 = 4 + 8 × 19.442 = 4 + 155.538 = 159.538

Is the number 378 a Perfect Square?

The prime factorization of 378 = 2¹ × 3³ × 7¹. Here, the prime factor 2 is not in the pair. Therefore, 378 is not a perfect square.

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