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Square Root of 92

Did you know that 92 is a composite number which is divisible by 2 and 4? All composite numbers have more than two factors, apart from 1 and the number itself (92). In this lesson, we will learn to calculate the square root of 92 by long division method. We will also go through a few solved examples and interactive questions related to the square root of 92.

Square Root of 92: √92 = 9.591
Square of 92: 92² = 8,464

1.	What Is the Square Root of 92?
2.	Is Square Root of 92 Rational or Irrational?
3.	How to Find the Square Root of 92?
4.	FAQs on Square Root of 92

What Is the Square Root of 92?

The number which on multiplication with itself gives the product as 92 is the square root of 92. As there is no such integer which on squaring gives 92, the square root of 92 is not a whole number.

Is the Square Root of 92 Rational or Irrational?

On taking the square root of 92, we get 9.591663 (approximately) as the result. The value obtained is a non-recurring and non-terminating decimal number. Thus, 92 is not a perfect square which also proves that the square root of 92 is an irrational number.

Tips and Tricks:

For any non-perfect square, the square root of that number will be an irrational number. As 92 is not a perfect square, its square root is an irrational number.

How to Find the Square Root of 92?

We can find the square root of 92 using the long division method.

Simplified Radical Form of Square Root of 92

92 can be written as the product of 2 and 46. It is given as:

√92 = √(2 × 46) = √(2 × 2 × 23) = 2√23

46 is expressed as the product of 2 and 23. The number which gets repeated within the square root is 2. Thus, the simplified radical form of the square root of 92 is 2√23.

Square Root of 92 by Long Division Method

The square root of 92 is found using the long division method. The steps to be followed are:

Step 1: We start pairing from the right and pair up the digits by placing a bar above them.
Step 2: We find a number such that on multiplication with itself, the product is less than or equal to 92. Keeping the divisor as 9, we get the quotient as 9 and the remainder 92-81 = 11.
Step 3: Double the divisor and enter it with a blank on its right. Then assume the largest digit to replace the blank. This will become the new digit in the quotient. Now, when the new divisor will be multiplied to the new quotient, the final product will be lesser than or equal to our dividend. Finally, divide and write the remainder. Repeat this process to get the decimal places you want.

Thus, √92 = 9.591

Explore square roots using illustrations and interactive examples

Challenging Questions:

How will Christie find the square root of 92 using the long division method up to 8 decimal places?
How will Mandy express the square root of 460 in terms of square root of 92?

Example 1: What is the length of a square box with area 92 square inches rounded to the nearest tenth?

Solution
The area of a square is given as (length)².
Hence, area = (length)² = 92 ⇒ length = √92 = 9.59 ≈ 9.6 inches.
The length of a square box with area 92 square inches rounded to nearest tenth is 9.6 inches.
Example 2: Evaluate (√92 + 2√23)/(4√23 - √92)

Solution
As we know, √92 can be simplified as 2√23.
(√92 + 2√23) = (2√23 + 2√23) = 4√23
(4√23 - √92) = (4√23 - 2√23) = 2√23
Thus, (√92 + 2√23)/(4√23 - √92) ⇒ 4√23/ 2√23 = 2.

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FAQs on Square Root of 92

What is the square root of 92 in the simplest form?

The square root of 92 in the simplest form is 2√23.

How do you find the square root of 92?

92 is not a perfect square number. Hence, the square root of 92 can obtained by using the long division method.

What is the approximate square root of 92?

The square root of 92 is 9.5916 (approximately).

Is the square root of 92 rational or irrational?

The square root of 92 is irrational.

Is the square root of 92 a real number?

Yes, the square root of 92 is a real number.

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