Square Root of 42
The number 42 is a number with three prime factors 2, 3, and 7. So, its prime factorization. The square root of a number is both positive and negative. We will now calculate the square root of 42 using various methods and learn a few interesting facts and questions as well.
- Square root of 42: 6.48074
- Square of 42: 1764
|1.||What Is the Square Root of 42?|
|2.||Is Square Root of 42 Rational or Irrational?|
|3.||How to Find the Square Root of 42?|
|4.||FAQs on Square Root of 42|
|5.||Important Notes on Square Root of 42|
What Is the Square Root of 42?
- The square root of a number implies a number whose product with itself gives the initial number.
- The square root of 42 is 6.4807.
- The square root of 42 is written as √42 in radical form and it cannot be reduced further.
- The square root of 42 can be written as (42)1/2 in exponential form.
Is Square Root of 42 Rational or Irrational?
A rational number is a number that can be expressed in the form of p/q where q ≠ 0.
And the square root of 42 cannot be expressed in the form of p/q.
So, the square root of 42 is an irrational number.
How to Find the Square Root of 42?
We will now calculate the square root of 42 using these methods:
Square Root of 42 Using Approximation Method
- Find two consecutive perfect squares between which the number 42 lies. The two numbers are 36 (62) and 49 (72).
So, the whole number part of the square root of 42 will be 6.
- Now, for the decimal part we will use the formula:
(Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square)
= (42 - 36)/(49 - 36) = 6/13 = 0.461
- So, the estimated square root of 42 by the approximation method is 6.461.
Square Root of 42 by Long Division
Now we will calculate the square root of 42 by the long division method.
- Start pairing the digits from the right side by putting a bar on top of them. In this case, we only have one pair (42).
- Now find a number(z) such that z × z ≤ 42. So, z will be 6 as 6 × 6 = 36 ≤ 42.
- We get both the quotient and remainder as 6. Now, we will add the divisor z with itself and get the new divisor (12).
- Put a decimal in the dividend and quotient part after 6 simultaneously. Also, put 3 pairs of zero in the dividend part after the decimal.
- Bring down one pair of zero. Hence, our dividend becomes 600. Find a number(m) such that 12m × m ≤ 600. The number m will be 4 as 124 × 4 = 496 ≤ 600.
- Now repeat the above step for the remaining two pairs of zeros.
So, we get the square root of √42 = 6.480 by the long division method.
Explore square roots using illustrations and interactive examples.
- The number 42 is not a perfect square.
- The square root of -42 is an imaginary number.
- The square root of 42 is an irrational number.
Square Root of 42 Solved Examples
Example 1: Alex is riding her car at a speed of √42 m/s. By how much she should increase her speed so that she can cover 1 km in 100 seconds?
Required speed = 1000/100 = 10 m/s
Her current speed = √42 m/s
Therefore, she will have to increase her speed by = 10 - √42 = 10 – 6.48 = 3.52 m/s
Example 2: What is the smallest multiple of 42 which is a perfect square?
A perfect square is a number whose factors are the square of a number.
The prime factorization of 42: 2 × 3 × 7
To make it a perfect square we have to make the pairs of 2, 3, and 7.
Therefore the multiple of 42 which is a perfect square will be 42 × 2 × 3 × 7
That is the square of 42 = 1764.
FAQs on Square Roots of 42
What is the negative square root of 42?
The negative square root of 42 is -6.4807.
What is the square of 42?
The square of 42 is (42)2 = 1764.
Can we find the square root of 42 using the prime factorization form?
No, we can’t find the square root of 42 by the prime factorization method as it cannot be reduced further.
Because the number 42 has three prime factors 2, 3, and 7.
Can we calculate the square root of 42 using the repeated subtraction method?
No, we cannot find the square root of 42 using the repeated subtraction method.
Because that method can be used only to numbers with square root as integers.
Is the number 42 a perfect square?
No, the number 42 is not a perfect square
Because the square root of 42 is a non-terminating and non-repeating number.