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Square Root of 351

The square root of 351 is expressed as √351 in the radical form and as (351)^½ or (351)^0.5 in the exponent form. The square root of 351 rounded up to 10 decimal places is 18.7349939952. It is the positive solution of the equation x² = 351. We can express the square root of 351 in its lowest radical form as 3 √39.

Square Root of 351: 18.734993995195193
Square Root of 351 in exponential form: (351)^½ or (351)^0.5
Square Root of 351 in radical form: √351 or 3 √39

Square Root of 351

1.	What is the Square Root of 351?
2.	How to find the Square Root of 351?
3.	Is the Square Root of 351 Irrational?
4.	FAQs

What is the Square Root of 351?

The square root of 351, (or root 351), is the number which when multiplied by itself gives the product as 351. Therefore, the square root of 351 = √351 = 3 √39 = 18.734993995195193.

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How to Find Square Root of 351?

Square Root of 351 by Long Division Method

Value of √351 by Long Division Method

Explanation:

Forming pairs: 03 and 51
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 51, to the right of the remainder 2. The new dividend is now 251.
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 8) such that 2Z × Z <= 251. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 251.
Divide 251 by 28 with the quotient as 8, giving the remainder = 251 - 28 × 8 = 251 - 224 = 27.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 7) such that 36Z × Z <= 2700. Together they form a new divisor (367) for the new dividend (2700).
Divide 2700 by 367 with the quotient as 7, giving the remainder = 2700 - 367 × 7 = 2700 - 2569 = 131.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 351.

Therefore, the square root of 351 by long division method is 18.7 approx.

Is Square Root of 351 Irrational?

The actual value of √351 is undetermined. The value of √351 up to 25 decimal places is 18.73499399519519461754068. Hence, the square root of 351 is an irrational number.

☛ Also Check:

Square Root of 109 - √109 = 10.44031
Square Root of 105 - √105 = 10.24695
Square Root of 34 - √34 = 5.83095
Square Root of 29 - √29 = 5.38516
Square Root of 1000 - √1000 = 31.62278
Square Root of 13 - √13 = 3.60555
Square Root of 97 - √97 = 9.84886

Square Root of 351 Solved Examples

Example 1: Solve the equation x² − 351 = 0

Solution:

x² - 351 = 0 i.e. x² = 351
x = ±√351
Since the value of the square root of 351 is 18.735,
⇒ x = +√351 or -√351 = 18.735 or -18.735.
Example 2: If the area of an equilateral triangle is 351√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 = 351√3 in²
⇒ a = ±√1404 in
Since length can't be negative,
⇒ a = √1404 = 2 √351
We know that the square root of 351 is 18.735.
⇒ a = 37.470 in
Example 3: If the area of a square is 351 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 = 351 in²
⇒ a = ±√351 in
Since length can't be negative,
⇒ a = √351 = 18.735 in

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FAQs on the Square Root of 351

What is the Value of the Square Root of 351?

The square root of 351 is 18.73499.

Why is the Square Root of 351 an Irrational Number?

Upon prime factorizing 351 i.e. 3³ × 13¹, 3 is in odd power. Therefore, the square root of 351 is irrational.

What is the Value of 3 square root 351?

The square root of 351 is 18.735. Therefore, 3 √351 = 3 × 18.735 = 56.205.

If the Square Root of 351 is 18.735. Find the Value of the Square Root of 3.51.

Let us represent √3.51 in p/q form i.e. √(351/100) = 3.51/10 = 1.873. Hence, the value of √3.51 = 1.873

Is the number 351 a Perfect Square?

The prime factorization of 351 = 3³ × 13¹. Here, the prime factor 3 is not in the pair. Therefore, 351 is not a perfect square.

What is the Square Root of 351 in Simplest Radical Form?

We need to express 351 as the product of its prime factors i.e. 351 = 3 × 3 × 3 × 13. Therefore, √351 = √3 × 3 × 3 × 13 = 3 √39. Thus, the square root of 351 in the lowest radical form is 3 √39.

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