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Square Root of 93

The square root of 93 is expressed as √93 in the radical form and as (93)^½ or (93)^0.5 in the exponent form. The square root of 93 rounded up to 7 decimal places is 9.6436508. It is the positive solution of the equation x² = 93.

Square Root of 93: 9.643650760992955
Square Root of 93 in exponential form: (93)^½ or (93)^0.5
Square Root of 93 in radical form: √93

Square Root of 93

1.	What is the Square Root of 93?
2.	How to find the Square Root of 93?
3.	Is the Square Root of 93 Irrational?
4.	FAQs

What is the Square Root of 93?

The square root of 93, (or root 93), is the number which when multiplied by itself gives the product as 93. Therefore, the square root of 93 = √93 = 9.643650760992955.

☛ Check: Square Root Calculator

How to Find Square Root of 93?

Square Root of 93 by Long Division Method

Value of √93 by Long Division Method

Explanation:

Forming pair: 93
Find a number Y (9) such that whose square is <= 93. Now divide 93 by 9 with quotient as 9.
Now, let's find the decimal places after the quotient 9.
Bring down the next pair 00, to the right of the remainder 12. The new dividend is now 1200.
Add the last digit of the quotient (9) to the divisor (9) i.e. 9 + 9 = 18. To the right of 18, find a digit Z (which is 6) such that 18Z × Z <= 1200. After finding Z, together 18 and Z (6) form a new divisor 186 for the new dividend 1200.
Divide 1200 by 186 with the quotient as 6, giving the remainder = 1200 - 186 × 6 = 1200 - 1116 = 84.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 93.

Therefore, the square root of 93 by long division method is 9.64 approx.

Is Square Root of 93 Irrational?

The actual value of √93 is undetermined. The value of √93 up to 25 decimal places is 9.643650760992954995760031. Hence, the square root of 93 is an irrational number.

☛ Also Check:

Square Root of 61 - √61 = 7.81025
Square Root of 250 - √250 = 15.81139
Square Root of 289 - √289 = 17
Square Root of 841 - √841 = 29
Square Root of 512 - √512 = 22.62742
Square Root of 74 - √74 = 8.60233
Square Root of 99 - √99 = 9.94987

Square Root of 93 Solved Examples

Example 1: Solve the equation x² − 93 = 0

Solution:

x² - 93 = 0 i.e. x² = 93
x = ±√93
Since the value of the square root of 93 is 9.644,
⇒ x = +√93 or -√93 = 9.644 or -9.644.
Example 2: If the area of a square is 93 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 = 93 in²
⇒ a = ±√93 in
Since length can't be negative,
⇒ a = √93 = 9.644 in
Example 3: If the surface area of a sphere is 372π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 372π in²
⇒ r = ±√93 in
Since radius can't be negative,
⇒ r = √93
The square root of 93 is 9.644.
⇒ r = 9.644 in

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FAQs on the Square Root of 93

What is the Value of the Square Root of 93?

The square root of 93 is 9.64365.

Why is the Square Root of 93 an Irrational Number?

Upon prime factorizing 93 i.e. 3¹ × 31¹, 3 is in odd power. Therefore, the square root of 93 is irrational.

Evaluate 16 plus 8 square root 93

The given expression is 16 + 8 √93. We know that the square root of 93 is 9.644. Therefore, 16 + 8 √93 = 16 + 8 × 9.644 = 16 + 77.149 = 93.149

What is the Value of 18 square root 93?

The square root of 93 is 9.644. Therefore, 18 √93 = 18 × 9.644 = 173.586.

What is the Square Root of -93?

The square root of -93 is an imaginary number. It can be written as √-93 = √-1 × √93 = i √93 = 9.643i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 93 in Simplest Radical Form?

We need to express 93 as the product of its prime factors i.e. 93 = 3 × 31. Therefore, as visible, the radical form of the square root of 93 cannot be simplified further. Therefore, the simplest radical form of the square root of 93 can be written as √93

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