Square Root Of 42 Simplified

Square Root of 42

The number 42 is a number with three prime factors 2, 3, and seven. And so, its prime number factorization. The square root of a number is both positive and negative. We will at present summate the square root of 42 using various methods and acquire a few interesting facts and questions likewise.

Foursquare root of 42: 6.48074
Foursquare of 42: 1764

What Is the Foursquare 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 grade and it cannot be reduced further.
The foursquare root of 42 tin can be written every bit (42)^ane/2 in exponential form.

Is Square Root of 42 Rational or Irrational?

A rational number is a number that can be expressed in the grade of p/q where q ≠ 0.
And the square root of 42 cannot exist expressed in the class of p/q.
So, the square root of 42 is an irrational number.

How to Notice 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 ii sequent perfect squares betwixt which the number 42 lies. The two numbers are 36 (half dozen²) and 49 (7ⁱⁱ).
So, the whole number part of the square root of 42 will be 6.
Now, for the decimal part nosotros volition use the formula:
(Given number - Smaller perfect foursquare) / (Greater perfect square - smaller perfect square)
= (42 - 36)/(49 - 36) = half-dozen/13 = 0.461
So, the estimated square root of 42 by the approximation method is 6.461.

Square Root of 42 by Long Partition

At present we volition calculate the foursquare root of 42 by the long segmentation method.

Commencement pairing the digits from the right side by putting a bar on peak of them. In this case, nosotros only have 1 pair (42).
At present find a number(z) such that z × z ≤ 42. And then, z volition be 6 equally 6 × vi = 36 ≤ 42.
We get both the caliber and remainder as six. At present, we will add the divisor z with itself and get the new divisor (12).
Put a decimal in the dividend and caliber part afterwards 6 simultaneously. Besides, put 3 pairs of zero in the dividend function 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 volition be 4 as 124 × four = 496 ≤ 600.
Now echo the in a higher place stride for the remaining two pairs of zeros.

Square root of 42

So, we get the square root of √42 = 6.480 by the long division method.

Explore square roots using illustrations and interactive examples.

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Important Notes:

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.

Example ane: Alex is riding her auto at a speed of √42 grand/s. Past how much she should increase her speed and then that she can embrace ane km in 100 seconds?

Solution:
Required speed = 1000/100 = 10 chiliad/south
Her current speed = √42 thou/s
Therefore, she volition have to increment her speed by = ten - √42 = x – 6.48 = three.52 m/due south
Instance ii: What is the smallest multiple of 42 which is a perfect square?

Solution:
A perfect square is a number whose factors are the foursquare 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 × iii × 7
That is the square of 42 = 1764.

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FAQs on Foursquare Roots of 42

What is the negative foursquare root of 42?

The negative foursquare root of 42 is -6.4807.

What is the foursquare of 42?

The square of 42 is (42)^two = 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 farther.
Because the number 42 has iii prime factors 2, 3, and 7.

Tin we calculate the foursquare root of 42 using the repeated subtraction method?

No, nosotros cannot find the square root of 42 using the repeated subtraction method.
Considering 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.