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Square Root of 345

The square root of 345 is expressed as √345 in the radical form and as (345)^½ or (345)^0.5 in the exponent form. The square root of 345 rounded up to 9 decimal places is 18.574175621. It is the positive solution of the equation x² = 345.

Square Root of 345: 18.57417562100671
Square Root of 345 in exponential form: (345)^½ or (345)^0.5
Square Root of 345 in radical form: √345

Square Root of 345

1.	What is the Square Root of 345?
2.	How to find the Square Root of 345?
3.	Is the Square Root of 345 Irrational?
4.	FAQs

What is the Square Root of 345?

The square root of 345, (or root 345), is the number which when multiplied by itself gives the product as 345. Therefore, the square root of 345 = √345 = 18.57417562100671.

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How to Find Square Root of 345?

Square Root of 345 by Long Division Method

Value of √345 by Long Division Method

Explanation:

Forming pairs: 03 and 45
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 45, to the right of the remainder 2. The new dividend is now 245.
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 <= 245. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 245.
Divide 245 by 28 with the quotient as 8, giving the remainder = 245 - 28 × 8 = 245 - 224 = 21.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 21. The new dividend is now 2100.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 5) such that 36Z × Z <= 2100. Together they form a new divisor (365) for the new dividend (2100).
Divide 2100 by 365 with the quotient as 5, giving the remainder = 2100 - 365 × 5 = 2100 - 1825 = 275.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 345.

Therefore, the square root of 345 by long division method is 18.5 approximately.

Is Square Root of 345 Irrational?

The actual value of √345 is undetermined. The value of √345 up to 25 decimal places is 18.57417562100670997098569. Hence, the square root of 345 is an irrational number.

☛ Also Check:

Square Root of 21 - √21 = 4.58258
Square Root of 325 - √325 = 18.02776
Square Root of 19 - √19 = 4.35890
Square Root of 116 - √116 = 10.77033
Square Root of 28 - √28 = 5.29150
Square Root of 2 - √2 = 1.41421
Square Root of 169 - √169 = 13

Square Root of 345 Solved Examples

Example 1: Solve the equation x² − 345 = 0

Solution:

x² - 345 = 0 i.e. x² = 345
x = ±√345
Since the value of the square root of 345 is 18.574,
⇒ x = +√345 or -√345 = 18.574 or -18.574.
Example 2: If the area of a circle is 345π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 345π in²
⇒ r = ±√345 in
Since radius can't be negative,
⇒ r = √345
The square root of 345 is 18.574.
⇒ r = 18.574 in
Example 3: If the surface area of a cube is 2070 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 = 2070 in²
⇒ a = ±√345 in
Since length can't be negative,
⇒ a = √345
We know that the square root of 345 is 18.574.
⇒ a = 18.574 in

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FAQs on the Square Root of 345

What is the Value of the Square Root of 345?

The square root of 345 is 18.57417.

Why is the Square Root of 345 an Irrational Number?

Upon prime factorizing 345 i.e. 3¹ × 5¹ × 23¹, 3 is in odd power. Therefore, the square root of 345 is irrational.

Is the number 345 a Perfect Square?

The prime factorization of 345 = 3¹ × 5¹ × 23¹. Here, the prime factor 3 is not in the pair. Therefore, 345 is not a perfect square.

If the Square Root of 345 is 18.574. Find the Value of the Square Root of 3.45.

Let us represent √3.45 in p/q form i.e. √(345/100) = 3.45/10 = 1.857. Hence, the value of √3.45 = 1.857

What is the Value of 12 square root 345?

The square root of 345 is 18.574. Therefore, 12 √345 = 12 × 18.574 = 222.890.

What is the Square of the Square Root of 345?

The square of the square root of 345 is the number 345 itself i.e. (√345)² = (345)^2/2 = 345.

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