Question

what will be the root of 23?
pls tell me in detail.​

Answer 1

Answer:

Irrational number

Step-by-step explanation:

root of 23 is an irrational number

Hopefully

Brainliest

Answer 2

The square root of 23 is a number which, when multiplied by itself, results in the number 23. 23 is also a prime number, which makes it trickier to calculate its square root.

Square Root of 23: √23 = 4.79583152...

Square of 23: 232 = 529

What Is the Square Root of 23?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 23 can be written in multiple ways.

Radical form: √23

Decimal form: 4.796

Exponent form: (23)1/2

Is Square Root of 23 Rational or Irrational?

23 is a number that is not a perfect square, meaning it does not have a natural number as its square root.

Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 23 is an irrational number.

How to Find the Square Root of 23?

There are only 2 ways to find the square root of 23:

Long Division Method

Estimation and Approximation

We cannot use 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 consists of the following steps:

Step 1: Starting from the right, we will pair up the digits 23 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.

Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 23. The number 4 fits here as 4 squared gives 16. Dividing 23 by 4 with the quotient as 4, we get the remainder as 7.

Step 3: Drag a pair of 0s down and fill it next to 7 to make the dividend 700.

Step 4: Double the divisor 4, and enter 8 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 8X and X results in a value less than or equal to 700. Since 7 fits the value of X, we fill 7 in the quotient after the decimal point. Divide and write the remainder.

Step 5: Repeat this process to get the decimal places you want.

Square root of 23

Therefore, the square root of 23 = 4.7958

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

Step 1: Find a perfect square which is smaller than and bigger than 23. In this case, 4 and 5 will work as their squares are 16 and 25.

Step 2: Writing in terms of inequality- 4<√23<5 = 16<23<25

Step 3: Multiply by 10 and write in terms of square roots- √1600<√2300<√2500

Step 4: Move closer to inequality- √2209<√2300<√2304 = 47<10√23<48

= 4.7<√23<4.8

Step 5: Taking the average of upper and lower limits we get, (4.7 + 4.8)/2 = 4.75

Therefore, we can estimate the square root of 23 ≅ 4.75

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