The square source of 23 is expressed as √23 in the radical form and as (23)½ or (23)0.5 in the exponent form. The square source of 23 rounded up to 7 decimal locations is 4.7958315. The is the positive solution of the equation x2 = 23.

You are watching: Square root of 23 rational or irrational

Square source of 23: 4.795831523312719Square source of 23 in exponential form: (23)½ or (23)0.5Square root of 23 in radical form: √23
1.What Is the Square root of 23?
2.Is Square root of 23 reasonable or Irrational?
3.How to find the Square source of 23?
4.Important Notes
5.Think Tank
6.FAQs top top Square source of 23

What Is the Square source of 23?

The square source of a number n is created as √n. This number when squared or multiply by itself outcomes in the original number n. The square root of 23 have the right to be written in multiple ways.

Radical form: √23 Decimal form: 4.796Exponent form: (23)1/2

Is Square source of 23 reasonable or Irrational?

23 is a number the is no a perfect square, meaning it go not have a natural number together its square root.

How to find the Square root of 23?

There are just 2 methods to discover the square source of 23:

Long division MethodEstimation and Approximation

We cannot usage the prime factorization method here, as 23 is a prime number. Think about it.

Long division Method

The square root of 23 by long division method is composed of the following steps:

Step 1: Starting native the right, we will certainly pair up the digits 23 by placing a bar over them. We additionally pair the 0s in decimals in bag of 2 from left to right.Step 3: Drag a pair of 0s down and also fill it beside 7 to make the dividend 700.Step 4: twin the divisor 4, and enter 8 below with a blank digit top top its right. Guess the largest possible digit(X) to to fill in the blank and the quotient because that which the product the 8X and also X outcomes in a value much less than or same to 700. Since 7 fits the value of X, we fill 7 in the quotient ~ the decimal point. Divide and write the remainder. Step 5: Repeat this process to acquire the decimal locations you want.


Therefore, the square root of 23 = 4.7958

Estimation and Approximation

The estimation method offers us an almost right answer and is usually not accurate to more than 1 decimal place. However, the is easy to execute as deserve to be seen under.

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Step 1: find a perfect square i beg your pardon is smaller sized than and bigger than 23. In this case, 4 and also 5 will work as your squares room 16 and 25.Step 2: creating in terms of inequality- 4Step 3: main point by 10 and write in regards to square roots- √1600Step 4: move closer come inequality- √2209= 4.7Step 5: acquisition the typical of upper and also lower borders we get, (4.7 + 4.8)/2 = 4.75

Therefore, we deserve to estimate the square root of 23 ≅ 4.75

Explore square roots making use of illustrations and also interactive examples

Important Notes

There exists a optimistic and negative root of 23, 4.7958 and also -4.7958.The square root of 23 is one irrational number the is non-terminating.There will certainly be n/2 digits in the square source of an even number v n digits.There will certainly be (n+2)/2 number in the square source of an odd number with n digits.

Think Tank

Can friend think of a quadratic equation that has actually a root of √23?Since (-(√23)2 = 23, can we say the -√23 is likewise a square root of 23?