Square Root of 43
The square root of 43 is expressed as √43 in the radical form and as (43)½ or (43)0.5 in the exponent form. The square root of 43 rounded up to 8 decimal places is 6.55743852. It is the positive solution of the equation x2 = 43.
- Square Root of 43: 6.557438524302
- Square Root of 43 in exponential form: (43)½ or (43)0.5
- Square Root of 43 in radical form: √43
| 1. | What is the Square Root of 43? |
| 2. | Is Square Root of 43 Rational or Irrational? |
| 3. | How to Find the Square Root of 43? |
| 4. | FAQs on Square Root of 43 |
What is the Square Root of 43?
The square root of a number is a number which when multiplied by itself, results in the original number. For example, the square root of 25 is 5, as 5 times 5 results in 25 which makes it a perfect square. However, you can also have square roots of some numbers that do not result in whole numbers, such as 43. We can express the square root of 43 in different ways as:
- Decimal form: 6.557
- Radical form: √43
- Exponent form: (43)1/2
Is the Square Root of 43 Rational or Irrational?
- 43 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 43 is an irrational number.
How to Find the Square Root of 43?
Since we concluded that the square root of 43 is non-terminating, we can only use 2 methods to calculate the value of its square root
- Long Division Method
- Estimation and Approximation Method
Long Division Method
- Step 1: Starting from the right, we will pair up the digits 43 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
- Step 2: Think of a number whose square is less than or equal to 43. In this case, that number would be 6.
- Step 3: Dividing by 43 by 6 with quotient set as 6, we get a remainder of 7.
- Step 4: Drag a pair of 0’s down and fill it next to 7 to make the dividend 700.
- Step 5: The divisor, in this case 6 is doubled and written below. Now, we have 12X as the new divisor, and we need to find a value of X that makes the product of 12X × X less than or equal to 700. In this case, 125 is the required value
- Step 6: The number 5 is placed in the quotient after a decimal place. The new divisor for the next division will be 125 + 5 = 130.
Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.
Therefore, the square root of 43 = 6.557
Estimation and Approximation Method
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 that is smaller than and bigger than 43. In this case, 6 and 7 will work as their squares are 36 and 49.
- Step 2: Writing in terms of inequality- 6 < √43 < 7 = 36 < 43 < 49
- Step 3: Multiply by 100 and write in terms of square roots- √3600 < √4300 < √4900
- Step 4: Move closer to inequality- √4225 < √4300 < √4356 = 65 < 10√43 < 66 = 6.5 < √43 < 6.6
- Step 5: Taking average of upper and lower limits we get, (6.5 + 6.6)/2 = 6.55
Therefore, we can estimate the square root of 43 ≅ 6.55
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Challenging Questions
- Determine the value of the following:
- √0.43
- √4343
- What are the roots of -43? Also find the value of the square of the negative root of -43.
Important Notes
- The real roots of √43 are ± 6.557.
- There will be n/2 digits in the square root of an even number with n digits.
- There will be (n+2)/2 digits in the square root of an odd number with n digits.
FAQs on the Square Root of 43
What is the Value of the Square Root of 43?
The square root of 43 is 6.55743.
Why is the Square Root of 43 an Irrational Number?
The number 43 is prime. This implies that the number 43 is pairless and is not in the power of 2. Therefore, the square root of 43 is irrational.
Evaluate 15 plus 5 square root 43
The given expression is 15 + 5 √43. We know that the square root of 43 is 6.557. Therefore, 15 + 5 √43 = 15 + 5 × 6.557 = 15 + 32.787 = 47.787
What is the Square Root of -43?
The square root of -43 is an imaginary number. It can be written as √-43 = √-1 × √43 = i √43 = 6.557i
where i = √-1 and it is called the imaginary unit.
If the Square Root of 43 is 6.557. Find the Value of the Square Root of 0.43.
Let us represent √0.43 in p/q form i.e. √(43/100) = 0.43/10 = 0.656. Hence, the value of √0.43 = 0.656
What is the Square Root of 43 in Simplest Radical Form?
The number 43 is a prime number. This implies that the number 43 is pairless and is not in the power of 2. Therefore, the radical form of square root of 43 cannot be simplified further.