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Square Root of 94

The square root of 94 is expressed as √94 in the radical form and as (94)^½ or (94)^0.5 in the exponent form. The square root of 94 rounded up to 10 decimal places is 9.6953597148. It is the positive solution of the equation x² = 94.

Square Root of 94: 9.695359714832659
Square Root of 94 in exponential form: (94)^½ or (94)^0.5
Square Root of 94 in radical form: √94

Square Root of 94

1.	What is the Square Root of 94?
2.	How to find the Square Root of 94?
3.	Is the Square Root of 94 Irrational?
4.	FAQs

What is the Square Root of 94?

The square root of 94, (or root 94), is the number which when multiplied by itself gives the product as 94. Therefore, the square root of 94 = √94 = 9.695359714832659.

☛ Check: Square Root Calculator

How to Find Square Root of 94?

Square Root of 94 by Long Division Method

Value of √94 by Long Division Method

Explanation:

Forming pair: 94
Find a number Y (9) such that whose square is <= 94. Now divide 94 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 13. The new dividend is now 1300.
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 <= 1300. After finding Z, together 18 and Z (6) form a new divisor 186 for the new dividend 1300.
Divide 1300 by 186 with the quotient as 6, giving the remainder = 1300 - 186 × 6 = 1300 - 1116 = 184.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 94.

Therefore, the square root of 94 by long division method is 9.6 approx.

Is Square Root of 94 Irrational?

The actual value of √94 is undetermined. The value of √94 up to 25 decimal places is 9.695359714832658028148881. Hence, the square root of 94 is an irrational number.

☛ Also Check:

Square Root of 105 - √105 = 10.24695
Square Root of 22 - √22 = 4.69042
Square Root of 14 - √14 = 3.74166
Square Root of 10 - √10 = 3.16228
Square Root of 52 - √52 = 7.21110
Square Root of 19 - √19 = 4.35890
Square Root of 16 - √16 = 4

Square Root of 94 Solved Examples

Example 1: Solve the equation x² − 94 = 0

Solution:

x² - 94 = 0 i.e. x² = 94
x = ±√94
Since the value of the square root of 94 is 9.695,
⇒ x = +√94 or -√94 = 9.695 or -9.695.
Example 2: If the area of a square is 94 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 = 94 in²
⇒ a = ±√94 in
Since length can't be negative,
⇒ a = √94 = 9.695 in
Example 3: If the area of a circle is 94π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 94π in²
⇒ r = ±√94 in
Since radius can't be negative,
⇒ r = √94
The square root of 94 is 9.695.
⇒ r = 9.695 in

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FAQs on the Square Root of 94

What is the Value of the Square Root of 94?

The square root of 94 is 9.69535.

Why is the Square Root of 94 an Irrational Number?

Upon prime factorizing 94 i.e. 2¹ × 47¹, 2 is in odd power. Therefore, the square root of 94 is irrational.

Is the number 94 a Perfect Square?

The prime factorization of 94 = 2¹ × 47¹. Here, the prime factor 2 is not in the pair. Therefore, 94 is not a perfect square.

What is the Value of 20 square root 94?

The square root of 94 is 9.695. Therefore, 20 √94 = 20 × 9.695 = 193.907.

What is the Square Root of 94 in Simplest Radical Form?

We need to express 94 as the product of its prime factors i.e. 94 = 2 × 47. Therefore, as visible, the radical form of the square root of 94 cannot be simplified further. Therefore, the simplest radical form of the square root of 94 can be written as √94

What is the Square Root of -94?

The square root of -94 is an imaginary number. It can be written as √-94 = √-1 × √94 = i √94 = 9.695i
where i = √-1 and it is called the imaginary unit.

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