# Square Root of 46

## Is 46 a Perfect Square?

In mathematics, we classify 46 as a perfect square when the square root of 46 is an integer.

In this instance, as we will observe in the computations below, we can ascertain that 46 is not a perfect square.

Take a look at our list of 1000 perfect squares, and read more about them to find out what they are.

## Is the Square Root of 46 a Rational or Irrational Number?

The common question is whether the square root of a number is irrational or rational. Irrational numbers cannot be written as a fraction, while rational numbers can.

If it is a rational number, then it is not a perfect square. A quick way to check this is to see if it is 46, a perfect square.

Since we are aware that 46 is a perfect square, it follows that the square root of 46 is an irrational number.

## Is it Possible to Simplify the Square Root of 46?

This is a process called simplifying surd, where you cannot simplify the square root of 46 in this example if you can only make the radical symbol inside 46.

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The square root of 46 is already in its simplest radical form.

## How to Determine the Square Root of 46 Using a Calculator

If you have a calculator, the simplest way to calculate the square root of 46 is by pressing the √x key and then typing 46.

The square root of 46 is approximately equal to 6.7823.

## How to Determine the Square Root of 46 using a Computer

You can calculate the square root using the SQRT function in Google Sheets or Excel Numbers on a computer.

The square root of 46 is approximately equal to 6.782329983125.

## What is the Rounded Square Root of 46?

Sometimes, you might need to round the square root of a certain number down to 46 decimal places. The solutions, if required, are available here.

10th: The square root of 46 is approximately 6.8.

100th: The square root of 46 is approximately 6.78.

1000th: √46. is approximately equal to 6.782.

## What is the Fractional Equivalent of the Square Root of 46?

We discussed earlier in this article that solely a rational number can be expressed as a fraction, while irrational numbers cannot.

We can approximate the square root of 46 to the nearest hundredth by converting it into an appropriate fraction. However, since the square root of 46 is an irrational number, we cannot convert it into an exact fraction as mentioned earlier.

√46.

≈ 6.8/1.

≈ 678/100.

Approximately6.and 39/50.

## What is the Exponential Form of the Square Root of 46?

Let’s see how to do calculations involving square roots, which can be converted to a number called the base with a fractional exponent.

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The square root of b is equal to the square root of b raised to the power of 1/2.

√46. = 46½

## How to Determine the Square Root of 46 Using Long Division

Before mathematicians knew how to calculate the square root of a number, computers and calculators were invented, making it very useful for solving long division problems and testing. Finally, we can use the division method to calculate the square root of 46.

### First Step

.Decimal one want we because 00 of set one and left to right from digits two of pairs in 46 up Set

### Second Step

In this way, place6.at the bottom and 36 on the top. Hence, the square root of 36 is 6, and the greatest ideal square smaller than or equal to 46 is 36, commencing with the initial group.

6.

### Third Step

Subtract 36 from 46 and write the result below. Then proceed to the next set of numbers.

6.

### Fourth Step

Double the number in green on top:6.× 2 = 12. Then, use 12 and the bottom number to make this problem:

12 times a number is less than or equal to 1000.

7 is can be number largest the found we error and trial with. “Blank” same the and “blank” are marks question the.

Now, input the number 7 at the top:

6.7

The last two steps actually repeat the previous two steps. The notice is that the square root of 46 has an accuracy of one decimal digit. The answer is shown at the top in green! That’s it. The last two steps actually repeat the previous two steps. You can simply add decimal places to your answer by adding more sets of 00.

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