How do you find the square root of 42?

If a number is multiplied by itself and gives the result as 42, then the number is the square root 42 . The square root of 42 is symbolically expressed as √42. Thus, if we multiply the number 6.4807 two times, we get the original value 42. Square Root of 42 in Decimal Form: 6.481.

How do you find the perfect square of 42?

Solution: A perfect square is a number whose factors are the square of a number. To make it a perfect square we have to make the pairs of 2, 3, and 7 . That is the square of 42=1764.

How do you find the square root answer?

Here are the steps to finding the square root using factoring: Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. ... Separate the factors into their own square roots. ... Solve for the individual squares. ... Finish solving the equation. Aug 8, 2022

Which number is closest to √ 42?

Explanation: To find the two whole numbers closest to √42, we can calculate the square roots of the numbers around 42. The square root of 36 is 6, and the square root of 49 is 7. Since 42 is closer to 49, the two whole numbers closest to √42 are 6 and 7 .

What is the simplest form of √42?

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.

What is the trick to find square root?

Step 1: Pair the digits from right to left, 404 01. Step 2: Check the unit digit of the number and compare it with the above table . Here, the unit digit is 1, thus possible unit digits for the square root of 40401 is 1 and 9. But the square root of 1 is 1, thus unit digit will have 1.

How to find square root by hand?

How to find the square root of a number and calculate it by hand STEP 1: Separate The Digits Into Pairs. To begin, let's organize the workspace. ... STEP 2: Find The Largest Integer. ... STEP 3: Now Subtract That Integer. ... STEP 4: Let's Move To The Next Pair. ... STEP 5: Find The Right Match. ... STEP 6: Subtract Again. Feb 7, 2020

Solution: To find the square of 42, we multiply it by itself i.e. 42. Therefore, the square of 42 is 1764 .

What is the square root of 42 to the nearest ten?

Answer. Answer: 6.48 or 6.5 rounded up!

What is the square root of 42 to one decimal place?

Find the square root of 42 correct to one place of decimalthe answer is 6.5 .

What is the answer to the square of 42?

Solution: To find the square of 42, we multiply it by itself i.e. 42. Therefore, the square of 42 is 1764 .

What is the simplified form of √40?

If we know the prime factorization of 40, we can write the simplest radical form of the square root of 40. Thus, the prime factorization of 40 is 2 × 2 × 2 × 5. If it is written in the radical form (i.e) √2×√2×√2×√5, we get the simplest radical form of the square root of 40. (i.e) 2√10 .

Square Root of 42 - How to Find the Square Root of 42? (2024)

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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 sideby 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.

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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.

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?
Solution:
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
See Also
Square Root of 40 - How to Find the Square Root of 40?
Example 2: What is the smallest multiple of 42 which is a perfect square?
Solution:
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.

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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.