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Square root of 96

The square root of the number 96 is a number whose product with itself gives 96. The square root of a number can be positive or negative, real or imaginary. Now we will calculate the square root of 96 using various methods and a few interesting facts and problems as well.

Square root of 96: √96 = 9.79796
Square of 96: (96)² = 9216

1.	What Is the Square Root of 96?
2.	Is Square Root of 96 Rational or Irrational?
3.	How to Find the Square Root of 96?
4.	FAQs on Square Root of 96
5.	Important Notes on Square Root of 96

What Is the Square Root of 96?

The square root of 96 is written as √96 = 9.79796
The square root of 96 can also be written as 4√6 in simplified form.
The square root of number 96 is not an integer so, it is not a perfect square.

Is the Square Root of 96 Rational or Irrational?

A number is known as a rational if it can be written in the form of p/q where q ≠ 0.
The square root of 96 is a non-repeating and non-terminating number.
So, the square root of 96 is an irrational number.

How to Find the Square Root of 96?

We will now find the square root of 96 using the following methods.

Square Root of 96 Using Prime Factorization Method

Prime factorization of 96: 2⁵ × 3
Prime factors of 96 in pairs: (2 × 2) × (2 × 2) × 2 × 3
Square of 96 is √96: √ ((2 × 2)² × 6)
√96 = ±4√6

Square Root of 96 by Long Division

We will now find the square root of 96 by the long division method.

Start grouping the digits from the unit’s place in pairs of two digits by putting a bar/line on top of them. We have pair in this case (96).
Find a number (a) such that a × a ≤ 96. So, a will be 9 as 9 × 9 = 81.
We get 15 (96-81) as the remainder and 9 as the quotient. Now add the divisor a with itself to get the new divisor (9+9 =18).
Put a decimal in the quotient and dividend part simultaneously. Also, put 3 pairs of zero in the dividend part after the decimal.
Bring down one pair of zero. Now our new dividend is 1500. Now find a number (b) such that 18b × b ≤ 1500. The number m will be 7 as 187 × 7 = 1309 ≤ 1500.
Repeat the above step for the remaining two pairs of zeros.

Square Root of 96

So, we get the square root of √96 = 9.797 by the long division method.

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Important Notes:

The square root of 96 is an irrational number.
The square root of -96 is an imaginary number.
The number 96 is not a perfect square.

Challenging Questions

Find the value of √√96.
Find the square root of all the factors of 96 except 1 and 96.

Example 1: Estimate the square root of 96 using the approximation method.

Solution:
The number 96 lies between 81 and 100 (two consecutive perfect squares).
So, the whole number part of the square root of 96 is 9.
For the decimal part we will use the formula: (96 – 81)/(100 – 81) = 15/19 = 0.7894
Therefore, the square root of 96 is 9.7894 approx.
Example 2: Rio wants to find the relationship between the square root of 96 and 6. Can you help Rio?

Solution:
The square root of 96 in simplified form is 4√6.
We can see that the square root of 96 is four times the square root of 6.
So, the square root of 96 = 4 × square root of 6.
Example 3: Find the smallest multiple of 96 which is a perfect square?

Solution:
A perfect square is a number whose factors are squares of a number.
The prime factors of 96 in pairs = (2 × 2) × (2 × 2) × 2 × 3
Therefore, to make it a perfect square, we need to multiply it by 2.
So, 96 × 6 (576) is the multiple of 96 which is a perfect square.

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FAQs on Square Roots of 96

What is the negative square root of 96?

The negative square root of 96 is -9.79796.

What is the square root of 96 up to 7 decimal places?

The square root of 96 is √96 = 9.7979589

Can we find the square root of 96 using the repeated subtraction method?

No, we can’t find the square root of 96 using the repeated subtraction method.
The number 96 is not a perfect square and that method can be used only for perfect squares.

What is the square of 96?

The square of 96 is 9216.

How can we represent the square root of 96 in exponential and radical form?

The square root of 96 is written as √96 in radical form.
The square root of 96 is written as (96)^1/2 in exponential form.

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