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Square Root of 350

The square root of 350 is expressed as √350 in the radical form and as (350)^½ or (350)^0.5 in the exponent form. The square root of 350 rounded up to 5 decimal places is 18.70829. It is the positive solution of the equation x² = 350. We can express the square root of 350 in its lowest radical form as 5 √14.

Square Root of 350: 18.708286933869708
Square Root of 350 in exponential form: (350)^½ or (350)^0.5
Square Root of 350 in radical form: √350 or 5 √14

Square Root of 350

1.	What is the Square Root of 350?
2.	How to find the Square Root of 350?
3.	Is the Square Root of 350 Irrational?
4.	FAQs

What is the Square Root of 350?

The square root of 350, (or root 350), is the number which when multiplied by itself gives the product as 350. Therefore, the square root of 350 = √350 = 5 √14 = 18.708286933869708.

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How to Find Square Root of 350?

Square Root of 350 by Long Division Method

Value of √350 by Long Division Method

Explanation:

Forming pairs: 03 and 50
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 50, to the right of the remainder 2. The new dividend is now 250.
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 <= 250. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 250.
Divide 250 by 28 with the quotient as 8, giving the remainder = 250 - 28 × 8 = 250 - 224 = 26.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 26. The new dividend is now 2600.
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 <= 2600. Together they form a new divisor (367) for the new dividend (2600).
Divide 2600 by 367 with the quotient as 7, giving the remainder = 2600 - 367 × 7 = 2600 - 2569 = 31.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 350.

Therefore, the square root of 350 by long division method is 18.7 approx.

Is Square Root of 350 Irrational?

The actual value of √350 is undetermined. The value of √350 up to 25 decimal places is 18.70828693386970692791874. Hence, the square root of 350 is an irrational number.

☛ Also Check:

Square Root of 92 - √92 = 9.59166
Square Root of 97 - √97 = 9.84886
Square Root of 113 - √113 = 10.63015
Square Root of 52 - √52 = 7.21110
Square Root of 80 - √80 = 8.94427
Square Root of 22 - √22 = 4.69042
Square Root of 51 - √51 = 7.14143

Square Root of 350 Solved Examples

Example 1: Solve the equation x² − 350 = 0

Solution:

x² - 350 = 0 i.e. x² = 350
x = ±√350
Since the value of the square root of 350 is 18.708,
⇒ x = +√350 or -√350 = 18.708 or -18.708.
Example 2: If the area of a square is 350 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 = 350 in²
⇒ a = ±√350 in
Since length can't be negative,
⇒ a = √350 = 18.708 in
Example 3: If the area of an equilateral triangle is 350√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 = 350√3 in²
⇒ a = ±√1400 in
Since length can't be negative,
⇒ a = √1400 = 2 √350
We know that the square root of 350 is 18.708.
⇒ a = 37.417 in

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FAQs on the Square Root of 350

What is the Value of the Square Root of 350?

The square root of 350 is 18.70828.

Why is the Square Root of 350 an Irrational Number?

Upon prime factorizing 350 i.e. 2¹ × 5² × 7¹, 2 is in odd power. Therefore, the square root of 350 is irrational.

What is the Value of 17 square root 350?

The square root of 350 is 18.708. Therefore, 17 √350 = 17 × 18.708 = 318.041.

Evaluate 18 plus 8 square root 350

The given expression is 18 + 8 √350. We know that the square root of 350 is 18.708. Therefore, 18 + 8 √350 = 18 + 8 × 18.708 = 18 + 149.666 = 167.666

If the Square Root of 350 is 18.708. Find the Value of the Square Root of 3.5.

Let us represent √3.5 in p/q form i.e. √(350/100) = 3.5/10 = 1.871. Hence, the value of √3.5 = 1.871

Is the number 350 a Perfect Square?

The prime factorization of 350 = 2¹ × 5² × 7¹. Here, the prime factor 2 is not in the pair. Therefore, 350 is not a perfect square.

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